********************************************************************************
************** Testing random number generators and distributions **************
********************************************************************************
Using seed: 0x34f05c64d7ad598f

Quality testing basic random number generator cmb_random(), uniform on [0,1)
Drawing 1000000 samples...

Expected: N  1000000  Mean   0.5000  StdDev   0.2887  Variance  0.08333  Skewness    0.000  Kurtosis   -1.200
Actual:   N  1000000  Mean   0.4999  StdDev   0.2887  Variance  0.08335  Skewness 0.0009428  Kurtosis   -1.200
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,    0.05000)   |#################################################=
[   0.05000,     0.1000)   |#################################################=
[    0.1000,     0.1500)   |#################################################-
[    0.1500,     0.2000)   |#################################################=
[    0.2000,     0.2500)   |#################################################=
[    0.2500,     0.3000)   |#################################################=
[    0.3000,     0.3500)   |#################################################-
[    0.3500,     0.4000)   |#################################################=
[    0.4000,     0.4500)   |#################################################-
[    0.4500,     0.5000)   |#################################################=
[    0.5000,     0.5500)   |#################################################-
[    0.5500,     0.6000)   |#################################################=
[    0.6000,     0.6500)   |#################################################=
[    0.6500,     0.7000)   |#################################################=
[    0.7000,     0.7500)   |#################################################-
[    0.7500,     0.8000)   |#################################################-
[    0.8000,     0.8500)   |#################################################-
[    0.8500,     0.9000)   |##################################################
[    0.9000,     0.9500)   |#################################################=
[    0.9500,      1.000)   |#################################################=
[     1.000,   Infinity)   |
--------------------------------------------------------------------------------

Autocorrelation factors (expected 0.0):
           -1.0                              0.0                              1.0
--------------------------------------------------------------------------------
   1   0.002                                  |-
   2   0.001                                  |-
   3  -0.001                                 -|
   4   0.001                                  |-
   5   0.000                                  |-
   6  -0.000                                 -|
   7  -0.002                                 -|
   8   0.000                                  |-
   9  -0.000                                 -|
  10  -0.000                                 -|
  11   0.001                                  |-
  12   0.001                                  |-
  13  -0.000                                 -|
  14  -0.001                                 -|
  15  -0.000                                 -|
--------------------------------------------------------------------------------

Partial autocorrelation factors (expected 0.0):
           -1.0                              0.0                              1.0
--------------------------------------------------------------------------------
   1   0.002                                  |-
   2   0.001                                  |-
   3  -0.001                                 -|
   4   0.001                                  |-
   5   0.000                                  |-
   6  -0.000                                 -|
   7  -0.002                                 -|
   8   0.000                                  |-
   9  -0.000                                 -|
  10  -0.001                                 -|
  11   0.001                                  |-
  12   0.001                                  |-
  13  -0.000                                 -|
  14  -0.001                                 -|
  15  -0.000                                 -|
--------------------------------------------------------------------------------

Raw moment:   Expected:   Actual:   Error:
--------------------------------------------------------------------------------
    1             0.5     0.49992   -0.016 %
    2         0.33333     0.33327   -0.019 %
    3            0.25     0.24996   -0.014 %
    4             0.2     0.19999   -0.005 %
    5         0.16667     0.16667    0.004 %
    6         0.14286     0.14288    0.013 %
    7           0.125     0.12503    0.021 %
    8         0.11111     0.11114    0.026 %
    9             0.1     0.10003    0.031 %
   10        0.090909    0.090939    0.033 %
   11        0.083333    0.083361    0.034 %
   12        0.076923    0.076948    0.033 %
   13        0.071429    0.071451    0.031 %
   14        0.066667    0.066685    0.028 %
   15          0.0625    0.062515    0.024 %
--------------------------------------------------------------------------------
================================================================================

Quality testing cmb_random_uniform(-1,2)
Drawing 1000000 samples...

Expected: N  1000000  Mean   0.5000  StdDev   0.8660  Variance   0.7500  Skewness    0.000  Kurtosis   -1.200
Actual:   N  1000000  Mean   0.5000  StdDev   0.8658  Variance   0.7496  Skewness 0.001050  Kurtosis   -1.200
--------------------------------------------------------------------------------
( -Infinity,     -1.000)   |
[    -1.000,    -0.8000)   |#################################################=
[   -0.8000,    -0.6000)   |#################################################=
[   -0.6000,    -0.4000)   |#################################################=
[   -0.4000,    -0.2000)   |#################################################=
[   -0.2000,      0.000)   |#################################################=
[     0.000,     0.2000)   |#################################################=
[    0.2000,     0.4000)   |#################################################=
[    0.4000,     0.6000)   |#################################################=
[    0.6000,     0.8000)   |#################################################=
[    0.8000,      1.000)   |##################################################
[     1.000,      1.200)   |#################################################=
[     1.200,      1.400)   |#################################################=
[     1.400,      1.600)   |#################################################=
[     1.600,      1.800)   |#################################################=
[     1.800,      2.000)   |#################################################=
[     2.000,      2.200)   |
[     2.200,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing cmb_random_triangular(-1, 2, 3)
Drawing 1000000 samples...

Expected: N  1000000  Mean    1.333  StdDev   0.8498  Variance   0.7222  Skewness  -0.4224  Kurtosis  -0.6000
Actual:   N  1000000  Mean    1.334  StdDev   0.8503  Variance   0.7231  Skewness  -0.4218  Kurtosis  -0.6007
--------------------------------------------------------------------------------
( -Infinity,     -1.000)   |
[    -1.000,    -0.8000)   |#=
[   -0.8000,    -0.6000)   |#####-
[   -0.6000,    -0.4000)   |########=
[   -0.4000,    -0.2000)   |###########=
[   -0.2000,      0.000)   |###############=
[     0.000,     0.2000)   |##################=
[    0.2000,     0.4000)   |######################-
[    0.4000,     0.6000)   |##########################-
[    0.6000,     0.8000)   |#############################-
[    0.8000,      1.000)   |################################-
[     1.000,      1.200)   |####################################-
[     1.200,      1.400)   |#######################################=
[     1.400,      1.600)   |###########################################-
[     1.600,      1.800)   |##############################################-
[     1.800,      2.000)   |##################################################
[     2.000,      2.200)   |##############################################-
[     2.200,      2.400)   |####################################-
[     2.400,      2.600)   |##########################-
[     2.600,      2.800)   |###############=
[     2.800,      3.000)   |#####-
[     3.000,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing standard normal distribution, mean = 0, sigma = 1
Drawing 1000000 samples...

Expected: N  1000000  Mean    0.000  StdDev    1.000  Variance    1.000  Skewness    0.000  Kurtosis    0.000
Actual:   N  1000000  Mean 7.302e-05  StdDev    1.001  Variance    1.001  Skewness 0.004263  Kurtosis 0.0004018
--------------------------------------------------------------------------------
( -Infinity,     -5.000)   |
[    -5.000,     -4.500)   |-
[    -4.500,     -4.000)   |-
[    -4.000,     -3.500)   |-
[    -3.500,     -3.000)   |-
[    -3.000,     -2.500)   |#-
[    -2.500,     -2.000)   |####-
[    -2.000,     -1.500)   |###########=
[    -1.500,     -1.000)   |########################-
[    -1.000,    -0.5000)   |#######################################-
[   -0.5000,      0.000)   |#################################################=
[     0.000,     0.5000)   |##################################################
[    0.5000,      1.000)   |#######################################-
[     1.000,      1.500)   |#######################=
[     1.500,      2.000)   |###########-
[     2.000,      2.500)   |####-
[     2.500,      3.000)   |#-
[     3.000,      3.500)   |-
[     3.500,      4.000)   |-
[     4.000,      4.500)   |-
[     4.500,      5.000)   |-
[     5.000,   Infinity)   |
--------------------------------------------------------------------------------

Autocorrelation factors (expected 0.0):
           -1.0                              0.0                              1.0
--------------------------------------------------------------------------------
   1   0.001                                  |-
   2   0.001                                  |-
   3  -0.000                                 -|
   4   0.000                                  |-
   5   0.000                                  |-
   6  -0.001                                 -|
   7   0.001                                  |-
   8   0.001                                  |-
   9  -0.001                                 -|
  10   0.000                                  |-
  11  -0.002                                 -|
  12  -0.000                                 -|
  13   0.002                                  |-
  14   0.000                                  |-
  15  -0.001                                 -|
--------------------------------------------------------------------------------

Partial autocorrelation factors (expected 0.0):
           -1.0                              0.0                              1.0
--------------------------------------------------------------------------------
   1   0.001                                  |-
   2   0.001                                  |-
   3  -0.000                                 -|
   4   0.000                                  |-
   5   0.000                                  |-
   6  -0.001                                 -|
   7   0.001                                  |-
   8   0.001                                  |-
   9  -0.001                                 -|
  10   0.000                                  |-
  11  -0.002                                 -|
  12  -0.000                                 -|
  13   0.002                                  |-
  14   0.000                                  |-
  15  -0.001                                 -|
--------------------------------------------------------------------------------

                              Cimba ziggurat method:    Box Muller method:
Raw moment:     Expected:     Actual:     Error:        Actual:     Error:
--------------------------------------------------------------------------------
    1                 0     7.302e-05      ---        0.0005688      ---
    2                 1         1.001    0.147 %          1.001    0.064 %
    3                 0      0.004492      ---         0.002423      ---
    4                 3         3.009    0.307 %          3.002    0.053 %
    5                 0       0.05286      ---          0.01807      ---
    6                15         15.05    0.319 %          15.03    0.208 %
    7                 0        0.6819      ---           0.2543      ---
    8               105         104.8   -0.145 %          105.8    0.749 %
    9                 0         10.44      ---            5.742      ---
   10               945         929.8   -1.607 %          961.5    1.747 %
   11                 0         176.2      ---              147      ---
   12          1.04e+04          9909   -4.679 %      1.072e+04    3.130 %
   13                 0          3111      ---             3763      ---
   14         1.351e+05     1.218e+05   -9.862 %      1.414e+05    4.672 %
   15                 0     5.611e+04      ---        9.471e+04      ---
================================================================================

Quality testing normal distribution, mean = 2.000000, sigma = 1.000000
Drawing 1000000 samples...

Expected: N  1000000  Mean    2.000  StdDev    1.000  Variance    1.000  Skewness    0.000  Kurtosis    0.000
Actual:   N  1000000  Mean    2.000  StdDev    1.001  Variance    1.001  Skewness 0.003855  Kurtosis -0.0003901
--------------------------------------------------------------------------------
( -Infinity,     -4.000)   |
[    -4.000,     -3.000)   |-
[    -3.000,     -2.000)   |-
[    -2.000,     -1.000)   |-
[    -1.000,      0.000)   |###-
[     0.000,      1.000)   |###################=
[     1.000,      2.000)   |##################################################
[     2.000,      3.000)   |#################################################=
[     3.000,      4.000)   |###################=
[     4.000,      5.000)   |###-
[     5.000,      6.000)   |-
[     6.000,      7.000)   |-
[     7.000,      8.000)   |
[     8.000,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing standard exponential distribution, mean = 1
Drawing 1000000 samples...

Expected: N  1000000  Mean    1.000  StdDev    1.000  Variance    1.000  Skewness    2.000  Kurtosis    6.000
Actual:   N  1000000  Mean   0.9992  StdDev    1.001  Variance    1.001  Skewness    2.000  Kurtosis    5.954
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      1.000)   |##################################################
[     1.000,      2.000)   |##################-
[     2.000,      3.000)   |######=
[     3.000,      4.000)   |##=
[     4.000,      5.000)   |=
[     5.000,      6.000)   |-
[     6.000,      7.000)   |-
[     7.000,      8.000)   |-
[     8.000,      9.000)   |-
[     9.000,      10.00)   |-
[     10.00,      11.00)   |-
[     11.00,      12.00)   |-
[     12.00,      13.00)   |-
[     13.00,      14.00)   |
[     14.00,   Infinity)   |
--------------------------------------------------------------------------------

Autocorrelation factors (expected 0.0):
           -1.0                              0.0                              1.0
--------------------------------------------------------------------------------
   1   0.001                                  |-
   2   0.001                                  |-
   3  -0.000                                 -|
   4  -0.001                                 -|
   5  -0.001                                 -|
   6   0.000                                  |-
   7  -0.001                                 -|
   8   0.000                                  |-
   9   0.001                                  |-
  10  -0.001                                 -|
  11  -0.000                                 -|
  12   0.001                                  |-
  13   0.001                                  |-
  14  -0.001                                 -|
  15   0.001                                  |-
--------------------------------------------------------------------------------

Partial autocorrelation factors (expected 0.0):
           -1.0                              0.0                              1.0
--------------------------------------------------------------------------------
   1   0.001                                  |-
   2   0.001                                  |-
   3  -0.000                                 -|
   4  -0.001                                 -|
   5  -0.001                                 -|
   6   0.000                                  |-
   7  -0.001                                 -|
   8   0.000                                  |-
   9   0.001                                  |-
  10  -0.001                                 -|
  11  -0.000                                 -|
  12   0.001                                  |-
  13   0.001                                  |-
  14  -0.001                                 -|
  15   0.001                                  |-
--------------------------------------------------------------------------------
================================================================================

Quality testing exponential distribution, mean = 2.000000
Drawing 1000000 samples...

Expected: N  1000000  Mean    2.000  StdDev    2.000  Variance    4.000  Skewness    2.000  Kurtosis    6.000
Actual:   N  1000000  Mean    1.998  StdDev    1.999  Variance    3.996  Skewness    1.994  Kurtosis    5.891
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      2.000)   |##################################################
[     2.000,      4.000)   |##################-
[     4.000,      6.000)   |######=
[     6.000,      8.000)   |##-
[     8.000,      10.00)   |=
[     10.00,      12.00)   |-
[     12.00,      14.00)   |-
[     14.00,      16.00)   |-
[     16.00,      18.00)   |-
[     18.00,      20.00)   |-
[     20.00,      22.00)   |-
[     22.00,      24.00)   |-
[     24.00,      26.00)   |-
[     26.00,      28.00)   |-
[     28.00,      30.00)   |
[     30.00,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing cmb_random_erlang(5, 1)
Drawing 1000000 samples...

Expected: N  1000000  Mean    5.000  StdDev    2.236  Variance    5.000  Skewness   0.8944  Kurtosis    1.200
Actual:   N  1000000  Mean    4.998  StdDev    2.236  Variance    4.998  Skewness   0.8998  Kurtosis    1.224
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      2.000)   |#######=
[     2.000,      4.000)   |##############################################-
[     4.000,      6.000)   |##################################################
[     6.000,      8.000)   |##########################=
[     8.000,      10.00)   |##########-
[     10.00,      12.00)   |###-
[     12.00,      14.00)   |=
[     14.00,      16.00)   |-
[     16.00,      18.00)   |-
[     18.00,      20.00)   |-
[     20.00,      22.00)   |-
[     22.00,      24.00)   |-
[     24.00,      26.00)   |-
[     26.00,      28.00)   |
[     28.00,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing cmb_random_hypoexponential, k = 4, m = [1, 2, 4, 8]
Drawing 1000000 samples...

Expected: N  1000000  Mean    15.00  StdDev    9.220  Variance    85.00  Skewness    1.493  Kurtosis    ---  
Actual:   N  1000000  Mean    15.00  StdDev    9.217  Variance    84.96  Skewness    1.490  Kurtosis    3.569
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      6.000)   |##################=
[     6.000,      12.00)   |##################################################
[     12.00,      18.00)   |#######################################-
[     18.00,      24.00)   |######################-
[     24.00,      30.00)   |###########-
[     30.00,      36.00)   |#####=
[     36.00,      42.00)   |##=
[     42.00,      48.00)   |#-
[     48.00,      54.00)   |=
[     54.00,      60.00)   |-
[     60.00,      66.00)   |-
[     66.00,      72.00)   |-
[     72.00,      78.00)   |-
[     78.00,      84.00)   |-
[     84.00,      90.00)   |-
[     90.00,      96.00)   |-
[     96.00,      102.0)   |-
[     102.0,      108.0)   |-
[     108.0,      114.0)   |-
[     114.0,      120.0)   |
[     120.0,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing cmb_random_hyperexponential, k = 4, m = [1, 2, 4, 8], p = [0.1, 0.2, 0.3, 0.4]
Drawing 1000000 samples...

Expected: N  1000000  Mean    4.900  StdDev    6.212  Variance    38.59  Skewness    ---    Kurtosis    ---  
Actual:   N  1000000  Mean    4.897  StdDev    6.215  Variance    38.63  Skewness    2.817  Kurtosis    12.15
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      6.000)   |##################################################
[     6.000,      12.00)   |##########=
[     12.00,      18.00)   |####-
[     18.00,      24.00)   |#=
[     24.00,      30.00)   |=
[     30.00,      36.00)   |-
[     36.00,      42.00)   |-
[     42.00,      48.00)   |-
[     48.00,      54.00)   |-
[     54.00,      60.00)   |-
[     60.00,      66.00)   |-
[     66.00,      72.00)   |-
[     72.00,      78.00)   |-
[     78.00,      84.00)   |-
[     84.00,      90.00)   |-
[     90.00,      96.00)   |-
[     96.00,      102.0)   |-
[     102.0,      108.0)   |
[     108.0,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing cmb_random_weibull(2, 3)
Drawing 1000000 samples...

Expected: N  1000000  Mean    2.659  StdDev    1.390  Variance    1.931  Skewness    ---    Kurtosis    ---  
Actual:   N  1000000  Mean    2.660  StdDev    1.390  Variance    1.933  Skewness   0.6322  Kurtosis   0.2510
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      1.000)   |###################-
[     1.000,      2.000)   |##############################################-
[     2.000,      3.000)   |##################################################
[     3.000,      4.000)   |####################################-
[     4.000,      5.000)   |###################=
[     5.000,      6.000)   |########-
[     6.000,      7.000)   |##=
[     7.000,      8.000)   |=
[     8.000,      9.000)   |-
[     9.000,      10.00)   |-
[     10.00,      11.00)   |-
[     11.00,      12.00)   |-
[     12.00,      13.00)   |
[     13.00,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing gamma distribution, shape 3, scale 0.5
Drawing 1000000 samples...

Expected: N  1000000  Mean    1.500  StdDev   0.8660  Variance   0.7500  Skewness    1.155  Kurtosis    2.000
Actual:   N  1000000  Mean    1.501  StdDev   0.8676  Variance   0.7527  Skewness    1.154  Kurtosis    1.987
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,     0.5000)   |###############=
[    0.5000,      1.000)   |###############################################=
[     1.000,      1.500)   |##################################################
[     1.500,      2.000)   |####################################-
[     2.000,      2.500)   |######################-
[     2.500,      3.000)   |############-
[     3.000,      3.500)   |######-
[     3.500,      4.000)   |###-
[     4.000,      4.500)   |#=
[     4.500,      5.000)   |=
[     5.000,      5.500)   |-
[     5.500,      6.000)   |-
[     6.000,      6.500)   |-
[     6.500,      7.000)   |-
[     7.000,      7.500)   |-
[     7.500,      8.000)   |-
[     8.000,      8.500)   |-
[     8.500,      9.000)   |-
[     9.000,      9.500)   |-
[     9.500,      10.00)   |-
[     10.00,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing gamma distribution, shape 1, scale 1
Drawing 1000000 samples...

Expected: N  1000000  Mean    1.000  StdDev    1.000  Variance    1.000  Skewness    2.000  Kurtosis    6.000
Actual:   N  1000000  Mean    1.001  StdDev   0.9996  Variance   0.9992  Skewness    2.001  Kurtosis    6.043
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      1.000)   |##################################################
[     1.000,      2.000)   |##################-
[     2.000,      3.000)   |######=
[     3.000,      4.000)   |##-
[     4.000,      5.000)   |=
[     5.000,      6.000)   |-
[     6.000,      7.000)   |-
[     7.000,      8.000)   |-
[     8.000,      9.000)   |-
[     9.000,      10.00)   |-
[     10.00,      11.00)   |-
[     11.00,      12.00)   |-
[     12.00,      13.00)   |-
[     13.00,      14.00)   |-
[     14.00,      15.00)   |-
[     15.00,      16.00)   |
[     16.00,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing gamma distribution, shape 0.5, scale 2
Drawing 1000000 samples...

Expected: N  1000000  Mean    1.000  StdDev    1.414  Variance    2.000  Skewness    2.828  Kurtosis    12.00
Actual:   N  1000000  Mean   0.9998  StdDev    1.415  Variance    2.003  Skewness    2.843  Kurtosis    12.26
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      2.000)   |##################################################
[     2.000,      4.000)   |######=
[     4.000,      6.000)   |#=
[     6.000,      8.000)   |=
[     8.000,      10.00)   |-
[     10.00,      12.00)   |-
[     12.00,      14.00)   |-
[     14.00,      16.00)   |-
[     16.00,      18.00)   |-
[     18.00,      20.00)   |-
[     20.00,      22.00)   |-
[     22.00,      24.00)   |-
[     24.00,      26.00)   |-
[     26.00,      28.00)   |
[     28.00,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing gamma distribution, shape 0.1, scale 2
Drawing 1000000 samples...

Expected: N  1000000  Mean   0.2000  StdDev   0.6325  Variance   0.4000  Skewness    6.325  Kurtosis    60.00
Actual:   N  1000000  Mean   0.1991  StdDev   0.6283  Variance   0.3948  Skewness    6.244  Kurtosis    58.07
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      2.000)   |##################################################
[     2.000,      4.000)   |=
[     4.000,      6.000)   |-
[     6.000,      8.000)   |-
[     8.000,      10.00)   |-
[     10.00,      12.00)   |-
[     12.00,      14.00)   |-
[     14.00,      16.00)   |-
[     16.00,      18.00)   |-
[     18.00,      20.00)   |-
[     20.00,      22.00)   |-
[     22.00,      24.00)   |
[     24.00,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing log-normal distribution, m 1, s 0.5
Drawing 1000000 samples...

Expected: N  1000000  Mean    3.080  StdDev    1.642  Variance    2.695  Skewness    1.750  Kurtosis    5.898
Actual:   N  1000000  Mean    3.079  StdDev    1.639  Variance    2.687  Skewness    1.758  Kurtosis    6.006
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      2.000)   |##########################-
[     2.000,      4.000)   |##################################################
[     4.000,      6.000)   |###############=
[     6.000,      8.000)   |####-
[     8.000,      10.00)   |#-
[     10.00,      12.00)   |-
[     12.00,      14.00)   |-
[     14.00,      16.00)   |-
[     16.00,      18.00)   |-
[     18.00,      20.00)   |-
[     20.00,      22.00)   |-
[     22.00,      24.00)   |-
[     24.00,      26.00)   |-
[     26.00,      28.00)   |-
[     28.00,      30.00)   |
[     30.00,      32.00)   |-
[     32.00,      34.00)   |
[     34.00,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing logistic distribution, m 1, s 0.5
Drawing 1000000 samples...

Expected: N  1000000  Mean    1.000  StdDev   0.9069  Variance   0.8225  Skewness    0.000  Kurtosis    1.200
Actual:   N  1000000  Mean    1.002  StdDev   0.9077  Variance   0.8239  Skewness 0.005058  Kurtosis    1.236
--------------------------------------------------------------------------------
( -Infinity,     -6.000)   |
[    -6.000,     -5.000)   |-
[    -5.000,     -4.000)   |-
[    -4.000,     -3.000)   |-
[    -3.000,     -2.000)   |-
[    -2.000,     -1.000)   |##-
[    -1.000,      0.000)   |#############-
[     0.000,      1.000)   |#################################################=
[     1.000,      2.000)   |##################################################
[     2.000,      3.000)   |#############-
[     3.000,      4.000)   |##-
[     4.000,      5.000)   |-
[     5.000,      6.000)   |-
[     6.000,      7.000)   |-
[     7.000,      8.000)   |-
[     8.000,      9.000)   |-
[     9.000,      10.00)   |
[     10.00,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing cauchy distribution, m 1, s 0.5
Drawing 1000000 samples...

Expected: N  1000000  Mean    ---    StdDev    ---    Variance    ---    Skewness    ---    Kurtosis    ---  
Actual:   N  1000000  Mean    1.132  StdDev    372.0  Variance 1.383e+05  Skewness    609.8  Kurtosis 5.143e+05
--------------------------------------------------------------------------------
( -Infinity, -7.812e+04)   |
[-7.812e+04, -5.859e+04)   |-
[-5.859e+04, -3.906e+04)   |-
[-3.906e+04, -1.953e+04)   |-
[-1.953e+04,      0.000)   |########=
[     0.000,  1.953e+04)   |##################################################
[ 1.953e+04,  3.906e+04)   |-
[ 3.906e+04,  5.859e+04)   |
[ 5.859e+04,  7.812e+04)   |-
[ 7.812e+04,  9.764e+04)   |
[ 9.764e+04,  1.172e+05)   |-
[ 1.172e+05,  1.367e+05)   |
[ 1.367e+05,  1.562e+05)   |
[ 1.562e+05,  1.758e+05)   |
[ 1.758e+05,  1.953e+05)   |
[ 1.953e+05,  2.148e+05)   |
[ 2.148e+05,  2.343e+05)   |
[ 2.343e+05,  2.539e+05)   |
[ 2.539e+05,  2.734e+05)   |
[ 2.734e+05,  2.929e+05)   |
[ 2.929e+05,  3.125e+05)   |
[ 3.125e+05,   Infinity)   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing beta distribution, shape 2, scale 5
Drawing 1000000 samples...

Expected: N  1000000  Mean   0.2857  StdDev   0.1597  Variance  0.02551  Skewness   0.5963  Kurtosis  -0.1200
Actual:   N  1000000  Mean   0.2857  StdDev   0.1596  Variance  0.02549  Skewness   0.5982  Kurtosis  -0.1142
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,    0.05000)   |#############-
[   0.05000,     0.1000)   |#################################=
[    0.1000,     0.1500)   |#############################################-
[    0.1500,     0.2000)   |#################################################=
[    0.2000,     0.2500)   |#################################################=
[    0.2500,     0.3000)   |###############################################-
[    0.3000,     0.3500)   |#########################################=
[    0.3500,     0.4000)   |###################################-
[    0.4000,     0.4500)   |############################=
[    0.4500,     0.5000)   |######################-
[    0.5000,     0.5500)   |################-
[    0.5500,     0.6000)   |###########=
[    0.6000,     0.6500)   |#######=
[    0.6500,     0.7000)   |####=
[    0.7000,     0.7500)   |##=
[    0.7500,     0.8000)   |#-
[    0.8000,     0.8500)   |-
[    0.8500,     0.9000)   |-
[    0.9000,     0.9500)   |-
[    0.9500,      1.000)   |-
[     1.000,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing beta distribution, shape 2, scale 5, left 0, right 1
Drawing 1000000 samples...

Expected: N  1000000  Mean   0.2857  StdDev   0.1597  Variance  0.02551  Skewness   0.5963  Kurtosis  -0.1200
Actual:   N  1000000  Mean   0.2856  StdDev   0.1597  Variance  0.02552  Skewness   0.5976  Kurtosis  -0.1151
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,    0.05000)   |#############=
[   0.05000,     0.1000)   |#################################=
[    0.1000,     0.1500)   |#############################################-
[    0.1500,     0.2000)   |#################################################=
[    0.2000,     0.2500)   |##################################################
[    0.2500,     0.3000)   |###############################################-
[    0.3000,     0.3500)   |#########################################=
[    0.3500,     0.4000)   |###################################-
[    0.4000,     0.4500)   |############################=
[    0.4500,     0.5000)   |######################-
[    0.5000,     0.5500)   |################=
[    0.5500,     0.6000)   |###########=
[    0.6000,     0.6500)   |#######=
[    0.6500,     0.7000)   |####=
[    0.7000,     0.7500)   |##=
[    0.7500,     0.8000)   |#-
[    0.8000,     0.8500)   |-
[    0.8500,     0.9000)   |-
[    0.9000,     0.9500)   |-
[    0.9500,      1.000)   |-
[     1.000,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing beta distribution, shape 0.5, scale 2, left 0, right 1
Drawing 1000000 samples...

Expected: N  1000000  Mean   0.2000  StdDev   0.2138  Variance  0.04571  Skewness    1.247  Kurtosis   0.8182
Actual:   N  1000000  Mean   0.1998  StdDev   0.2136  Variance  0.04564  Skewness    1.247  Kurtosis   0.8199
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,    0.05000)   |##################################################
[   0.05000,     0.1000)   |###################-
[    0.1000,     0.1500)   |##############-
[    0.1500,     0.2000)   |###########-
[    0.2000,     0.2500)   |#########-
[    0.2500,     0.3000)   |#######=
[    0.3000,     0.3500)   |######=
[    0.3500,     0.4000)   |#####=
[    0.4000,     0.4500)   |#####-
[    0.4500,     0.5000)   |####-
[    0.5000,     0.5500)   |###=
[    0.5500,     0.6000)   |###-
[    0.6000,     0.6500)   |##=
[    0.6500,     0.7000)   |##-
[    0.7000,     0.7500)   |#=
[    0.7500,     0.8000)   |#-
[    0.8000,     0.8500)   |#-
[    0.8500,     0.9000)   |=
[    0.9000,     0.9500)   |-
[    0.9500,      1.000)   |-
[     1.000,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing beta distribution, shape 0.5, scale 0.5, left 2, right 5
Drawing 1000000 samples...

Expected: N  1000000  Mean    3.500  StdDev    1.061  Variance    1.125  Skewness    0.000  Kurtosis   -1.500
Actual:   N  1000000  Mean    3.500  StdDev    1.061  Variance    1.125  Skewness -0.0002863  Kurtosis   -1.500
--------------------------------------------------------------------------------
( -Infinity,      2.000)   |
[     2.000,      2.200)   |##################################################
[     2.200,      2.400)   |#####################-
[     2.400,      2.600)   |#################-
[     2.600,      2.800)   |###############-
[     2.800,      3.000)   |##############-
[     3.000,      3.200)   |#############-
[     3.200,      3.400)   |############=
[     3.400,      3.600)   |############=
[     3.600,      3.800)   |############=
[     3.800,      4.000)   |#############-
[     4.000,      4.200)   |#############=
[     4.200,      4.400)   |###############-
[     4.400,      4.600)   |#################-
[     4.600,      4.800)   |#####################=
[     4.800,      5.000)   |#################################################=
[     5.000,      5.200)   |
[     5.200,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing beta distribution, shape 0.1, scale 0.5, left -2, right 2
Drawing 1000000 samples...

Expected: N  1000000  Mean   -1.333  StdDev    1.179  Variance    1.389  Skewness    1.741  Kurtosis    1.615
Actual:   N  1000000  Mean   -1.333  StdDev    1.178  Variance    1.389  Skewness    1.741  Kurtosis    1.620
--------------------------------------------------------------------------------
( -Infinity,     -2.000)   |
[    -2.000,     -1.800)   |##################################################
[    -1.800,     -1.600)   |###=
[    -1.600,     -1.400)   |##-
[    -1.400,     -1.200)   |#=
[    -1.200,     -1.000)   |#-
[    -1.000,    -0.8000)   |#-
[   -0.8000,    -0.6000)   |#-
[   -0.6000,    -0.4000)   |#-
[   -0.4000,    -0.2000)   |=
[   -0.2000,      0.000)   |=
[     0.000,     0.2000)   |=
[    0.2000,     0.4000)   |=
[    0.4000,     0.6000)   |=
[    0.6000,     0.8000)   |=
[    0.8000,      1.000)   |=
[     1.000,      1.200)   |=
[     1.200,      1.400)   |=
[     1.400,      1.600)   |#-
[     1.600,      1.800)   |#-
[     1.800,      2.000)   |###-
[     2.000,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing PERT distribution, left 2, mode 5, right 10
Drawing 1000000 samples...

Expected: N  1000000  Mean    5.333  StdDev    1.491  Variance    2.222  Skewness   0.2236  Kurtosis  -0.6000
Actual:   N  1000000  Mean    5.334  StdDev    1.490  Variance    2.221  Skewness   0.2209  Kurtosis  -0.6031
--------------------------------------------------------------------------------
( -Infinity,      2.000)   |
[     2.000,      2.500)   |####-
[     2.500,      3.000)   |################-
[     3.000,      3.500)   |############################-
[     3.500,      4.000)   |######################################=
[     4.000,      4.500)   |##############################################=
[     4.500,      5.000)   |#################################################=
[     5.000,      5.500)   |##################################################
[     5.500,      6.000)   |##############################################=
[     6.000,      6.500)   |#########################################-
[     6.500,      7.000)   |##################################-
[     7.000,      7.500)   |##########################-
[     7.500,      8.000)   |##################-
[     8.000,      8.500)   |###########-
[     8.500,      9.000)   |#####-
[     9.000,      9.500)   |#=
[     9.500,      10.00)   |-
[     10.00,      10.50)   |
[     10.50,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing Pareto distribution, shape 3, scale 2
Drawing 1000000 samples...

Expected: N  1000000  Mean    3.000  StdDev    1.732  Variance    3.000  Skewness    ---    Kurtosis    ---  
Actual:   N  1000000  Mean    2.998  StdDev    1.710  Variance    2.924  Skewness    14.97  Kurtosis    1039.
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      14.00)   |##################################################
[     14.00,      28.00)   |-
[     28.00,      42.00)   |-
[     42.00,      56.00)   |-
[     56.00,      70.00)   |-
[     70.00,      84.00)   |-
[     84.00,      98.00)   |-
[     98.00,      112.0)   |-
[     112.0,      126.0)   |-
[     126.0,      140.0)   |-
[     140.0,      154.0)   |
[     154.0,      168.0)   |
[     168.0,      182.0)   |
[     182.0,      196.0)   |-
[     196.0,      210.0)   |
[     210.0,      224.0)   |
[     224.0,      238.0)   |
[     238.0,      252.0)   |
[     252.0,      266.0)   |
[     266.0,      280.0)   |-
[     280.0,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing chisquare distribution, v 4
Drawing 1000000 samples...

Expected: N  1000000  Mean    4.000  StdDev    2.828  Variance    8.000  Skewness    1.414  Kurtosis    3.000
Actual:   N  1000000  Mean    4.004  StdDev    2.826  Variance    7.984  Skewness    1.406  Kurtosis    2.935
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      2.000)   |#######################################=
[     2.000,      4.000)   |##################################################
[     4.000,      6.000)   |###############################-
[     6.000,      8.000)   |################-
[     8.000,      10.00)   |#######=
[     10.00,      12.00)   |###-
[     12.00,      14.00)   |#=
[     14.00,      16.00)   |=
[     16.00,      18.00)   |-
[     18.00,      20.00)   |-
[     20.00,      22.00)   |-
[     22.00,      24.00)   |-
[     24.00,      26.00)   |-
[     26.00,      28.00)   |-
[     28.00,      30.00)   |-
[     30.00,      32.00)   |-
[     32.00,      34.00)   |
[     34.00,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing f distribution, a 3, b 5
Drawing 1000000 samples...

Expected: N  1000000  Mean    1.667  StdDev    3.333  Variance    11.11  Skewness    ---    Kurtosis    ---  
Actual:   N  1000000  Mean    1.661  StdDev    3.147  Variance    9.903  Skewness    31.46  Kurtosis    3539.
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      30.00)   |##################################################
[     30.00,      60.00)   |-
[     60.00,      90.00)   |-
[     90.00,      120.0)   |-
[     120.0,      150.0)   |-
[     150.0,      180.0)   |-
[     180.0,      210.0)   |-
[     210.0,      240.0)   |-
[     240.0,      270.0)   |-
[     270.0,      300.0)   |
[     300.0,      330.0)   |
[     330.0,      360.0)   |-
[     360.0,      390.0)   |
[     390.0,      420.0)   |
[     420.0,      450.0)   |-
[     450.0,      480.0)   |-
[     480.0,      510.0)   |
[     510.0,      540.0)   |-
[     540.0,      570.0)   |
[     570.0,      600.0)   |-
[     600.0,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing Student's t distribution, v 3
Drawing 1000000 samples...

Expected: N  1000000  Mean    0.000  StdDev    1.732  Variance    3.000  Skewness    ---    Kurtosis    ---  
Actual:   N  1000000  Mean -0.001003  StdDev    1.721  Variance    2.963  Skewness   0.4689  Kurtosis    112.6
--------------------------------------------------------------------------------
( -Infinity,     -117.0)   |
[    -117.0,     -104.0)   |-
[    -104.0,     -91.00)   |
[    -91.00,     -78.00)   |
[    -78.00,     -65.00)   |-
[    -65.00,     -52.00)   |-
[    -52.00,     -39.00)   |-
[    -39.00,     -26.00)   |-
[    -26.00,     -13.00)   |-
[    -13.00,      0.000)   |#################################################=
[     0.000,      13.00)   |##################################################
[     13.00,      26.00)   |-
[     26.00,      39.00)   |-
[     39.00,      52.00)   |-
[     52.00,      65.00)   |-
[     65.00,      78.00)   |-
[     78.00,      91.00)   |
[     91.00,      104.0)   |
[     104.0,      117.0)   |-
[     117.0,      130.0)   |-
[     130.0,      143.0)   |
[     143.0,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing t distribution, m 1, s 2, v 3,
Drawing 1000000 samples...

Expected: N  1000000  Mean    1.000  StdDev    3.464  Variance    12.00  Skewness    ---    Kurtosis    ---  
Actual:   N  1000000  Mean   0.9936  StdDev    3.448  Variance    11.89  Skewness   0.7869  Kurtosis    254.9
--------------------------------------------------------------------------------
( -Infinity,     -256.0)   |
[    -256.0,     -224.0)   |-
[    -224.0,     -192.0)   |-
[    -192.0,     -160.0)   |
[    -160.0,     -128.0)   |-
[    -128.0,     -96.00)   |-
[    -96.00,     -64.00)   |-
[    -64.00,     -32.00)   |-
[    -32.00,      0.000)   |########################-
[     0.000,      32.00)   |##################################################
[     32.00,      64.00)   |-
[     64.00,      96.00)   |-
[     96.00,      128.0)   |-
[     128.0,      160.0)   |-
[     160.0,      192.0)   |
[     192.0,      224.0)   |
[     224.0,      256.0)   |
[     256.0,      288.0)   |
[     288.0,      320.0)   |
[     320.0,      352.0)   |
[     352.0,      384.0)   |
[     384.0,   Infinity)   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing Rayleigh distribution, s 1.5
Drawing 1000000 samples...

Expected: N  1000000  Mean    1.880  StdDev   0.9827  Variance   0.9657  Skewness   0.6311  Kurtosis   0.2451
Actual:   N  1000000  Mean    1.881  StdDev   0.9832  Variance   0.9667  Skewness   0.6340  Kurtosis   0.2514
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,     0.5000)   |#############=
[    0.5000,      1.000)   |#####################################-
[     1.000,      1.500)   |#################################################=
[     1.500,      2.000)   |##################################################
[     2.000,      2.500)   |#########################################=
[     2.500,      3.000)   |#############################-
[     3.000,      3.500)   |#################=
[     3.500,      4.000)   |#########=
[     4.000,      4.500)   |####=
[     4.500,      5.000)   |#=
[     5.000,      5.500)   |=
[     5.500,      6.000)   |-
[     6.000,      6.500)   |-
[     6.500,      7.000)   |-
[     7.000,      7.500)   |-
[     7.500,      8.000)   |-
[     8.000,      8.500)   |-
[     8.500,      9.000)   |
[     9.000,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================
************************* Integer-valued distributions *************************

Quality testing unbiased coin flip, p = 0.5
Drawing 1000000 samples...

Expected: N  1000000  Mean   0.5000  StdDev   0.5000  Variance   0.2500  Skewness    0.000  Kurtosis   -2.000
Actual:   N  1000000  Mean   0.4998  StdDev   0.5000  Variance   0.2500  Skewness 0.0007600  Kurtosis   -2.000
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,    0.05000)   |##################################################-
[   0.05000,     0.1000)   |
[    0.1000,     0.1500)   |
[    0.1500,     0.2000)   |
[    0.2000,     0.2500)   |
[    0.2500,     0.3000)   |
[    0.3000,     0.3500)   |
[    0.3500,     0.4000)   |
[    0.4000,     0.4500)   |
[    0.4500,     0.5000)   |
[    0.5000,     0.5500)   |
[    0.5500,     0.6000)   |
[    0.6000,     0.6500)   |
[    0.6500,     0.7000)   |
[    0.7000,     0.7500)   |
[    0.7500,     0.8000)   |
[    0.8000,     0.8500)   |
[    0.8500,     0.9000)   |
[    0.9000,     0.9500)   |
[    0.9500,      1.000)   |
[     1.000,   Infinity)   |#################################################=
--------------------------------------------------------------------------------
================================================================================

Quality testing biased Bernoulli trials, p = 0.6
Drawing 1000000 samples...

Expected: N  1000000  Mean   0.6000  StdDev   0.4899  Variance   0.2400  Skewness  -0.4082  Kurtosis   -1.833
Actual:   N  1000000  Mean   0.5995  StdDev   0.4900  Variance   0.2401  Skewness  -0.4060  Kurtosis   -1.835
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,    0.05000)   |#################################-
[   0.05000,     0.1000)   |
[    0.1000,     0.1500)   |
[    0.1500,     0.2000)   |
[    0.2000,     0.2500)   |
[    0.2500,     0.3000)   |
[    0.3000,     0.3500)   |
[    0.3500,     0.4000)   |
[    0.4000,     0.4500)   |
[    0.4500,     0.5000)   |
[    0.5000,     0.5500)   |
[    0.5500,     0.6000)   |
[    0.6000,     0.6500)   |
[    0.6500,     0.7000)   |
[    0.7000,     0.7500)   |
[    0.7500,     0.8000)   |
[    0.8000,     0.8500)   |
[    0.8500,     0.9000)   |
[    0.9000,     0.9500)   |
[    0.9500,      1.000)   |
[     1.000,   Infinity)   |##################################################
--------------------------------------------------------------------------------
================================================================================

Quality testing geometric distribution, p = 0.1
Drawing 1000000 samples...

Expected: N  1000000  Mean    10.00  StdDev    9.487  Variance    90.00  Skewness    2.003  Kurtosis    6.011
Actual:   N  1000000  Mean    10.01  StdDev    9.523  Variance    90.69  Skewness    2.020  Kurtosis    6.122
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      7.000)   |##################################################
[     7.000,      14.00)   |#############################=
[     14.00,      21.00)   |##############-
[     21.00,      28.00)   |######=
[     28.00,      35.00)   |###-
[     35.00,      42.00)   |#=
[     42.00,      49.00)   |=
[     49.00,      56.00)   |-
[     56.00,      63.00)   |-
[     63.00,      70.00)   |-
[     70.00,      77.00)   |-
[     77.00,      84.00)   |-
[     84.00,      91.00)   |-
[     91.00,      98.00)   |-
[     98.00,      105.0)   |-
[     105.0,      112.0)   |-
[     112.0,      119.0)   |-
[     119.0,      126.0)   |-
[     126.0,      133.0)   |-
[     133.0,      140.0)   |
[     140.0,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing binomial distribution, n = 10, p = 0.1
Drawing 1000000 samples...

Expected: N  1000000  Mean    1.000  StdDev   0.9487  Variance   0.9000  Skewness   0.8433  Kurtosis   0.5111
Actual:   N  1000000  Mean    1.000  StdDev   0.9492  Variance   0.9009  Skewness   0.8432  Kurtosis   0.5151
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,     0.5000)   |#############################################-
[    0.5000,      1.000)   |
[     1.000,      1.500)   |##################################################
[     1.500,      2.000)   |
[     2.000,      2.500)   |#########################-
[     2.500,      3.000)   |
[     3.000,      3.500)   |#######-
[     3.500,      4.000)   |
[     4.000,      4.500)   |#-
[     4.500,      5.000)   |
[     5.000,      5.500)   |-
[     5.500,      6.000)   |
[     6.000,      6.500)   |-
[     6.500,      7.000)   |
[     7.000,      7.500)   |-
[     7.500,      8.000)   |
[     8.000,      8.500)   |-
[     8.500,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing binomial distribution, n = 100, p = 0.5
Drawing 1000000 samples...

Expected: N  1000000  Mean    50.00  StdDev    5.000  Variance    25.00  Skewness    0.000  Kurtosis -0.02000
Actual:   N  1000000  Mean    49.99  StdDev    4.997  Variance    24.97  Skewness 0.001446  Kurtosis -0.01965
--------------------------------------------------------------------------------
( -Infinity,      24.00)   |
[     24.00,      27.00)   |-
[     27.00,      30.00)   |-
[     30.00,      33.00)   |-
[     33.00,      36.00)   |-
[     36.00,      39.00)   |#=
[     39.00,      42.00)   |#######-
[     42.00,      45.00)   |###################=
[     45.00,      48.00)   |#####################################-
[     48.00,      51.00)   |##################################################
[     51.00,      54.00)   |###############################################-
[     54.00,      57.00)   |###############################-
[     57.00,      60.00)   |##############=
[     60.00,      63.00)   |####=
[     63.00,      66.00)   |#-
[     66.00,      69.00)   |-
[     69.00,      72.00)   |-
[     72.00,      75.00)   |-
[     75.00,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing negative binomial (Pascal) distribution, m = 10, p = 0.1
Drawing 1000000 samples...

Expected: N  1000000  Mean    90.00  StdDev    30.00  Variance    900.0  Skewness   0.6333  Kurtosis   0.6011
Actual:   N  1000000  Mean    89.93  StdDev    29.98  Variance    898.9  Skewness   0.6305  Kurtosis   0.5960
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      17.00)   |-
[     17.00,      34.00)   |#=
[     34.00,      51.00)   |##############-
[     51.00,      68.00)   |####################################-
[     68.00,      85.00)   |##################################################
[     85.00,      102.0)   |##############################################=
[     102.0,      119.0)   |#################################-
[     119.0,      136.0)   |###################-
[     136.0,      153.0)   |#########=
[     153.0,      170.0)   |####-
[     170.0,      187.0)   |#=
[     187.0,      204.0)   |=
[     204.0,      221.0)   |-
[     221.0,      238.0)   |-
[     238.0,      255.0)   |-
[     255.0,      272.0)   |-
[     272.0,      289.0)   |-
[     289.0,      306.0)   |-
[     306.0,      323.0)   |-
[     323.0,      340.0)   |
[     340.0,   Infinity)   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing Poisson distribution, r = 5
Drawing 1000000 samples...

Expected: N  1000000  Mean    5.000  StdDev    2.236  Variance    5.000  Skewness   0.4472  Kurtosis   0.2000
Actual:   N  1000000  Mean    4.999  StdDev    2.234  Variance    4.989  Skewness   0.4524  Kurtosis   0.2085
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      1.000)   |#=
[     1.000,      2.000)   |#########-
[     2.000,      3.000)   |#######################=
[     3.000,      4.000)   |########################################-
[     4.000,      5.000)   |#################################################=
[     5.000,      6.000)   |##################################################
[     6.000,      7.000)   |#########################################-
[     7.000,      8.000)   |#############################=
[     8.000,      9.000)   |##################=
[     9.000,      10.00)   |##########-
[     10.00,      11.00)   |#####-
[     11.00,      12.00)   |##-
[     12.00,      13.00)   |=
[     13.00,      14.00)   |-
[     14.00,      15.00)   |-
[     15.00,      16.00)   |-
[     16.00,      17.00)   |-
[     17.00,      18.00)   |-
[     18.00,      19.00)   |-
[     19.00,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing Poisson distribution, r = 50
Drawing 1000000 samples...

Expected: N  1000000  Mean    50.00  StdDev    7.071  Variance    50.00  Skewness   0.1414  Kurtosis  0.02000
Actual:   N  1000000  Mean    49.99  StdDev    7.062  Variance    49.87  Skewness   0.1408  Kurtosis  0.01914
--------------------------------------------------------------------------------
( -Infinity,      20.00)   |
[     20.00,      24.00)   |-
[     24.00,      28.00)   |-
[     28.00,      32.00)   |=
[     32.00,      36.00)   |###-
[     36.00,      40.00)   |##########=
[     40.00,      44.00)   |#########################=
[     44.00,      48.00)   |##########################################=
[     48.00,      52.00)   |##################################################
[     52.00,      56.00)   |###########################################-
[     56.00,      60.00)   |###########################=
[     60.00,      64.00)   |#############-
[     64.00,      68.00)   |#####-
[     68.00,      72.00)   |#=
[     72.00,      76.00)   |-
[     76.00,      80.00)   |-
[     80.00,      84.00)   |-
[     84.00,      88.00)   |-
[     88.00,      92.00)   |-
[     92.00,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing Poisson distribution, r = 1e+13
Drawing 1000000 samples...

Expected: N  1000000  Mean 1.000e+13  StdDev 3.162e+06  Variance 1.000e+13  Skewness 3.162e-07  Kurtosis 1.000e-13
Actual:   N  1000000  Mean 1.000e+13  StdDev 3.162e+06  Variance 1.000e+13  Skewness 0.005064  Kurtosis -0.002520
--------------------------------------------------------------------------------
Bucket edges shown as offsets from base 9999984000000, bucket width 1.446e+06
--------------------------------------------------------------------------------
( -Infinity,  1.752e+05)   |
[ 1.752e+05,  1.621e+06)   |-
[ 1.621e+06,  3.066e+06)   |-
[ 3.066e+06,  4.512e+06)   |-
[ 4.512e+06,  5.957e+06)   |-
[ 5.957e+06,  7.403e+06)   |=
[ 7.403e+06,  8.849e+06)   |##-
[ 8.849e+06,  1.029e+07)   |######=
[ 1.029e+07,  1.174e+07)   |###############-
[ 1.174e+07,  1.319e+07)   |###########################=
[ 1.319e+07,  1.463e+07)   |#########################################-
[ 1.463e+07,  1.608e+07)   |##################################################
[ 1.608e+07,  1.752e+07)   |#################################################=
[ 1.752e+07,  1.897e+07)   |#######################################=
[ 1.897e+07,  2.041e+07)   |##########################-
[ 2.041e+07,  2.186e+07)   |#############=
[ 2.186e+07,  2.330e+07)   |######-
[ 2.330e+07,  2.475e+07)   |##-
[ 2.475e+07,  2.620e+07)   |=
[ 2.620e+07,  2.764e+07)   |-
[ 2.764e+07,  2.909e+07)   |-
[ 2.909e+07,   Infinity)   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing dice (discrete uniform) distribution, a = 1, b = 6
Drawing 1000000 samples...

Expected: N  1000000  Mean    3.500  StdDev    1.708  Variance    2.917  Skewness    0.000  Kurtosis   -1.269
Actual:   N  1000000  Mean    3.494  StdDev    1.707  Variance    2.916  Skewness 0.004635  Kurtosis   -1.268
--------------------------------------------------------------------------------
( -Infinity,      1.000)   |
[     1.000,      1.500)   |##################################################
[     1.500,      2.000)   |
[     2.000,      2.500)   |#################################################=
[     2.500,      3.000)   |
[     3.000,      3.500)   |#################################################=
[     3.500,      4.000)   |
[     4.000,      4.500)   |#################################################=
[     4.500,      5.000)   |
[     5.000,      5.500)   |#################################################=
[     5.500,      6.000)   |
[     6.000,      6.500)   |#################################################=
[     6.500,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing discrete non-uniform distribution, n = 7
Drawing 1000000 samples...

Expected: N  1000000  Mean    4.150  StdDev    1.768  Variance    3.127  Skewness  -0.7704  Kurtosis  -0.3742
Actual:   N  1000000  Mean    4.149  StdDev    1.769  Variance    3.129  Skewness  -0.7704  Kurtosis  -0.3741
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,     0.5000)   |########-
[    0.5000,      1.000)   |
[     1.000,      1.500)   |########-
[     1.500,      2.000)   |
[     2.000,      2.500)   |################=
[     2.500,      3.000)   |
[     3.000,      3.500)   |################=
[     3.500,      4.000)   |
[     4.000,      4.500)   |#################################-
[     4.500,      5.000)   |
[     5.000,      5.500)   |#################################-
[     5.500,      6.000)   |
[     6.000,      6.500)   |##################################################
[     6.500,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================

Quality testing vose alias sampling, n = 7
Drawing 1000000 samples...

Expected: N  1000000  Mean    4.150  StdDev    1.768  Variance    3.127  Skewness  -0.7704  Kurtosis  -0.3742
Actual:   N  1000000  Mean    4.147  StdDev    1.771  Variance    3.136  Skewness  -0.7696  Kurtosis  -0.3773
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,     0.5000)   |########-
[    0.5000,      1.000)   |
[     1.000,      1.500)   |########-
[     1.500,      2.000)   |
[     2.000,      2.500)   |################=
[     2.500,      3.000)   |
[     3.000,      3.500)   |################=
[     3.500,      4.000)   |
[     4.000,      4.500)   |#################################-
[     4.500,      5.000)   |
[     5.000,      5.500)   |#################################-
[     5.500,      6.000)   |
[     6.000,      6.500)   |##################################################
[     6.500,   Infinity)   |
--------------------------------------------------------------------------------
================================================================================
********************************************************************************
