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

Quality testing basic random number generator cmb_random(), uniform on [0,1]
Drawing 10000000 samples...

Expected: N 10000000  Mean   0.5000  StdDev   0.2887  Variance  0.08333  Skewness    0.000  Kurtosis   -1.200
Actual:   N 10000000  Mean   0.5000  StdDev   0.2887  Variance  0.08334  Skewness 0.0001143  Kurtosis   -1.200
--------------------------------------------------------------------------------
( -Infinity,  1.639e-08)   |
[ 1.639e-08,      1.000)   |##################################################
[     1.000,  Infinity )   |-
--------------------------------------------------------------------------------

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

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

Raw moment:   Expected:   Actual:   Error:
--------------------------------------------------------------------------------
    1             0.5     0.50003    0.007 %
    2         0.33333     0.33338    0.013 %
    3            0.25     0.25005    0.020 %
    4             0.2     0.20006    0.028 %
    5         0.16667     0.16672    0.035 %
    6         0.14286     0.14291    0.040 %
    7           0.125     0.12506    0.046 %
    8         0.11111     0.11117    0.050 %
    9             0.1     0.10005    0.053 %
   10        0.090909    0.090959    0.055 %
   11        0.083333     0.08338    0.056 %
   12        0.076923    0.076966    0.056 %
   13        0.071429    0.071468    0.055 %
   14        0.066667    0.066703    0.054 %
   15          0.0625    0.062533    0.053 %
--------------------------------------------------------------------------------
================================================================================

Quality testing cmb_random_uniform(-1,2)
Drawing 10000000 samples...

Expected: N 10000000  Mean   0.5000  StdDev   0.8660  Variance   0.7500  Skewness    0.000  Kurtosis   -1.200
Actual:   N 10000000  Mean   0.5002  StdDev   0.8661  Variance   0.7501  Skewness -0.0003735  Kurtosis   -1.200
--------------------------------------------------------------------------------
( -Infinity,     -1.000)   |
[    -1.000, -2.648e-07)   |#################################################=
[-2.648e-07,      1.000)   |##################################################-
[     1.000,      2.000)   |#################################################=
[     2.000,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing cmb_random_triangular(-1, 2, 3)
Drawing 10000000 samples...

Expected: N 10000000  Mean    1.333  StdDev   0.8498  Variance   0.7222  Skewness  -0.4224  Kurtosis  -0.6000
Actual:   N 10000000  Mean    1.333  StdDev   0.8497  Variance   0.7220  Skewness  -0.4218  Kurtosis  -0.5997
--------------------------------------------------------------------------------
( -Infinity,    -0.9986)   |
[   -0.9986,  0.0008767)   |##########-
[ 0.0008767,      1.000)   |#############################=
[     1.000,      2.000)   |#################################################=
[     2.000,      2.999)   |#############################=
[     2.999,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing standard normal distribution, mean = 0, sigma = 1
Drawing 10000000 samples...

Expected: N 10000000  Mean    0.000  StdDev    1.000  Variance    1.000  Skewness    0.000  Kurtosis    0.000
Actual:   N 10000000  Mean 0.0002365  StdDev   0.9997  Variance   0.9994  Skewness -0.0007746  Kurtosis 0.001622
--------------------------------------------------------------------------------
( -Infinity,     -5.146)   |
[    -5.146,     -4.198)   |-
[    -4.198,     -3.249)   |-
[    -3.249,     -2.301)   |#-
[    -2.301,     -1.352)   |##########=
[    -1.352,    -0.4040)   |###################################-
[   -0.4040,     0.5445)   |##################################################
[    0.5445,      1.493)   |##############################=
[     1.493,      2.441)   |########-
[     2.441,      3.390)   |=
[     3.390,      4.338)   |-
[     4.338,      5.287)   |-
[     5.287,  Infinity )   |-
--------------------------------------------------------------------------------

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

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

                              Cimba ziggurat method:    Box Muller method:
Raw moment:     Expected:     Actual:     Error:        Actual:     Error:
--------------------------------------------------------------------------------
    1                 0     0.0002365      ---       -0.0005908      ---
    2                 1        0.9994   -0.057 %         0.9994   -0.065 %
    3                 0    -6.482e-05      ---        -0.002157      ---
    4                 3         2.998   -0.060 %          2.997   -0.105 %
    5                 0     -0.007419      ---           -0.012      ---
    6                15            15    0.011 %          14.99   -0.037 %
    7                 0       -0.1112      ---         -0.08862      ---
    8               105         105.2    0.188 %          105.4    0.335 %
    9                 0        -1.323      ---          -0.8674      ---
   10               945         948.8    0.406 %          957.1    1.283 %
   11                 0        -12.23      ---           -10.37      ---
   12          1.04e+04     1.044e+04    0.409 %      1.071e+04    3.070 %
   13                 0        -26.91      ---           -132.7      ---
   14         1.351e+05     1.348e+05   -0.250 %       1.43e+05    5.807 %
   15                 0          2974      ---            -1701      ---
================================================================================

Quality testing normal distribution, mean = 2.000000, sigma = 1.000000
Drawing 10000000 samples...

Expected: N 10000000  Mean    2.000  StdDev    1.000  Variance    1.000  Skewness    0.000  Kurtosis    0.000
Actual:   N 10000000  Mean    2.000  StdDev    1.000  Variance   0.9999  Skewness 0.0001386  Kurtosis -0.001800
--------------------------------------------------------------------------------
( -Infinity,     -3.181)   |
[    -3.181,     -2.219)   |-
[    -2.219,     -1.258)   |-
[    -1.258,    -0.2962)   |#-
[   -0.2962,     0.6654)   |##########=
[    0.6654,      1.627)   |###################################=
[     1.627,      2.588)   |#################################################=
[     2.588,      3.550)   |#############################=
[     3.550,      4.512)   |#######-
[     4.512,      5.473)   |=
[     5.473,      6.435)   |-
[     6.435,      7.396)   |-
[     7.396,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing standard exponential distribution, mean = 1
Drawing 10000000 samples...

Expected: N 10000000  Mean    1.000  StdDev    1.000  Variance    1.000  Skewness    2.000  Kurtosis    6.000
Actual:   N 10000000  Mean    1.000  StdDev    1.000  Variance    1.000  Skewness    1.999  Kurtosis    5.986
--------------------------------------------------------------------------------
( -Infinity,  1.829e-07)   |
[ 1.829e-07,     0.9855)   |##################################################
[    0.9855,      1.971)   |##################=
[     1.971,      2.956)   |######=
[     2.956,      3.942)   |##=
[     3.942,      4.927)   |=
[     4.927,      5.913)   |-
[     5.913,      6.898)   |-
[     6.898,      7.884)   |-
[     7.884,      8.869)   |-
[     8.869,      9.855)   |-
[     9.855,      10.84)   |-
[     10.84,      11.83)   |-
[     11.83,      12.81)   |-
[     12.81,      13.80)   |-
[     13.80,      14.78)   |-
[     14.78,      15.77)   |-
[     15.77,      16.75)   |-
[     16.75,  Infinity )   |-
--------------------------------------------------------------------------------

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

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

Quality testing exponential distribution, mean = 2.000000
Drawing 10000000 samples...

Expected: N 10000000  Mean    2.000  StdDev    2.000  Variance    4.000  Skewness    2.000  Kurtosis    6.000
Actual:   N 10000000  Mean    2.000  StdDev    2.000  Variance    3.999  Skewness    1.996  Kurtosis    5.951
--------------------------------------------------------------------------------
( -Infinity,  7.369e-08)   |
[ 7.369e-08,      1.631)   |##################################################
[     1.631,      3.263)   |######################-
[     3.263,      4.894)   |#########=
[     4.894,      6.525)   |####-
[     6.525,      8.157)   |#=
[     8.157,      9.788)   |=
[     9.788,      11.42)   |-
[     11.42,      13.05)   |-
[     13.05,      14.68)   |-
[     14.68,      16.31)   |-
[     16.31,      17.94)   |-
[     17.94,      19.58)   |-
[     19.58,      21.21)   |-
[     21.21,      22.84)   |-
[     22.84,      24.47)   |-
[     24.47,      26.10)   |-
[     26.10,      27.73)   |-
[     27.73,      29.36)   |-
[     29.36,      31.00)   |-
[     31.00,      32.63)   |-
[     32.63,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing cmb_random_erlang(5, 1)
Drawing 10000000 samples...

Expected: N 10000000  Mean    5.000  StdDev    2.236  Variance    5.000  Skewness   0.8944  Kurtosis    1.200
Actual:   N 10000000  Mean    5.001  StdDev    2.237  Variance    5.003  Skewness   0.8958  Kurtosis    1.207
--------------------------------------------------------------------------------
( -Infinity,     0.1073)   |
[    0.1073,      1.369)   |##=
[     1.369,      2.631)   |########################-
[     2.631,      3.892)   |###############################################-
[     3.892,      5.154)   |##################################################
[     5.154,      6.416)   |######################################-
[     6.416,      7.677)   |########################-
[     7.677,      8.939)   |#############-
[     8.939,      10.20)   |######=
[     10.20,      11.46)   |###-
[     11.46,      12.72)   |#-
[     12.72,      13.99)   |=
[     13.99,      15.25)   |-
[     15.25,      16.51)   |-
[     16.51,      17.77)   |-
[     17.77,      19.03)   |-
[     19.03,      20.29)   |-
[     20.29,      21.56)   |-
[     21.56,      22.82)   |-
[     22.82,      24.08)   |-
[     24.08,      25.34)   |-
[     25.34,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing cmb_random_hypoexponential, k = 4, m = [1, 2, 4, 8]
Drawing 10000000 samples...

Expected: N 10000000  Mean    15.00  StdDev    9.220  Variance    85.00  Skewness    1.493  Kurtosis    ---  
Actual:   N 10000000  Mean    15.00  StdDev    9.223  Variance    85.06  Skewness    1.500  Kurtosis    3.680
--------------------------------------------------------------------------------
( -Infinity,     0.1033)   |
[    0.1033,      7.015)   |#######################-
[     7.015,      13.93)   |##################################################
[     13.93,      20.84)   |################################-
[     20.84,      27.75)   |###############=
[     27.75,      34.66)   |#######-
[     34.66,      41.58)   |###-
[     41.58,      48.49)   |#-
[     48.49,      55.40)   |=
[     55.40,      62.31)   |-
[     62.31,      69.22)   |-
[     69.22,      76.14)   |-
[     76.14,      83.05)   |-
[     83.05,      89.96)   |-
[     89.96,      96.87)   |-
[     96.87,      103.8)   |-
[     103.8,      110.7)   |-
[     110.7,      117.6)   |-
[     117.6,      124.5)   |-
[     124.5,      131.4)   |-
[     131.4,      138.3)   |-
[     138.3,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing cmb_random_hyperexponential, k = 4, m = [1, 2, 4, 8], p = [0.1, 0.2, 0.3, 0.4]
Drawing 10000000 samples...

Expected: N 10000000  Mean    4.900  StdDev    6.212  Variance    38.59  Skewness    ---    Kurtosis    ---  
Actual:   N 10000000  Mean    4.896  StdDev    6.205  Variance    38.51  Skewness    2.793  Kurtosis    11.82
--------------------------------------------------------------------------------
( -Infinity,  4.815e-08)   |
[ 4.815e-08,      6.388)   |##################################################
[     6.388,      12.78)   |##########-
[     12.78,      19.17)   |###=
[     19.17,      25.55)   |#-
[     25.55,      31.94)   |=
[     31.94,      38.33)   |-
[     38.33,      44.72)   |-
[     44.72,      51.11)   |-
[     51.11,      57.50)   |-
[     57.50,      63.88)   |-
[     63.88,      70.27)   |-
[     70.27,      76.66)   |-
[     76.66,      83.05)   |-
[     83.05,      89.44)   |-
[     89.44,      95.83)   |-
[     95.83,      102.2)   |-
[     102.2,      108.6)   |-
[     108.6,      115.0)   |-
[     115.0,      121.4)   |-
[     121.4,      127.8)   |
[     127.8,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing cmb_random_weibull(2, 3)
Drawing 10000000 samples...

Expected: N 10000000  Mean    2.659  StdDev    1.390  Variance    1.931  Skewness    ---    Kurtosis    ---  
Actual:   N 10000000  Mean    2.659  StdDev    1.390  Variance    1.932  Skewness   0.6303  Kurtosis   0.2414
--------------------------------------------------------------------------------
( -Infinity,  0.0001131)   |
[ 0.0001131,     0.9819)   |##################=
[    0.9819,      1.964)   |#############################################=
[     1.964,      2.945)   |##################################################
[     2.945,      3.927)   |#####################################-
[     3.927,      4.909)   |####################=
[     4.909,      5.891)   |########=
[     5.891,      6.872)   |##=
[     6.872,      7.854)   |=
[     7.854,      8.836)   |-
[     8.836,      9.818)   |-
[     9.818,      10.80)   |-
[     10.80,      11.78)   |-
[     11.78,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing gamma distribution, shape 3, scale 0.5
Drawing 10000000 samples...

Expected: N 10000000  Mean    1.500  StdDev   0.8660  Variance   0.7500  Skewness    1.155  Kurtosis    2.000
Actual:   N 10000000  Mean    1.500  StdDev   0.8662  Variance   0.7502  Skewness    1.155  Kurtosis    2.002
--------------------------------------------------------------------------------
( -Infinity,   0.001766)   |
[  0.001766,     0.9438)   |#################################=
[    0.9438,      1.886)   |##################################################
[     1.886,      2.828)   |######################-
[     2.828,      3.770)   |######=
[     3.770,      4.712)   |#=
[     4.712,      5.654)   |-
[     5.654,      6.596)   |-
[     6.596,      7.538)   |-
[     7.538,      8.480)   |-
[     8.480,      9.422)   |-
[     9.422,      10.36)   |-
[     10.36,      11.31)   |-
[     11.31,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing gamma distribution, shape 1, scale 1
Drawing 10000000 samples...

Expected: N 10000000  Mean    1.000  StdDev    1.000  Variance    1.000  Skewness    2.000  Kurtosis    6.000
Actual:   N 10000000  Mean   0.9996  StdDev   0.9998  Variance   0.9996  Skewness    2.002  Kurtosis    6.019
--------------------------------------------------------------------------------
( -Infinity,  3.061e-07)   |
[ 3.061e-07,     0.9746)   |##################################################
[    0.9746,      1.949)   |##################=
[     1.949,      2.924)   |#######-
[     2.924,      3.899)   |##=
[     3.899,      4.873)   |#-
[     4.873,      5.848)   |-
[     5.848,      6.823)   |-
[     6.823,      7.797)   |-
[     7.797,      8.772)   |-
[     8.772,      9.746)   |-
[     9.746,      10.72)   |-
[     10.72,      11.70)   |-
[     11.70,      12.67)   |-
[     12.67,      13.65)   |-
[     13.65,      14.62)   |-
[     14.62,      15.59)   |-
[     15.59,      16.57)   |
[     16.57,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing gamma distribution, shape 0.5, scale 2
Drawing 10000000 samples...

Expected: N 10000000  Mean    1.000  StdDev    1.414  Variance    2.000  Skewness    2.828  Kurtosis    12.00
Actual:   N 10000000  Mean    1.000  StdDev    1.415  Variance    2.003  Skewness    2.836  Kurtosis    12.12
--------------------------------------------------------------------------------
( -Infinity,  2.164e-14)   |
[ 2.164e-14,      1.310)   |#################################################=
[     1.310,      2.620)   |#########=
[     2.620,      3.930)   |###=
[     3.930,      5.240)   |#=
[     5.240,      6.551)   |=
[     6.551,      7.861)   |-
[     7.861,      9.171)   |-
[     9.171,      10.48)   |-
[     10.48,      11.79)   |-
[     11.79,      13.10)   |-
[     13.10,      14.41)   |-
[     14.41,      15.72)   |-
[     15.72,      17.03)   |-
[     17.03,      18.34)   |-
[     18.34,      19.65)   |-
[     19.65,      20.96)   |-
[     20.96,      22.27)   |-
[     22.27,      23.58)   |-
[     23.58,      24.89)   |-
[     24.89,      26.20)   |-
[     26.20,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing log-normal distribution, m 1, s 0.5
Drawing 10000000 samples...

Expected: N 10000000  Mean    3.080  StdDev    1.642  Variance    2.695  Skewness    1.750  Kurtosis    5.898
Actual:   N 10000000  Mean    3.080  StdDev    1.642  Variance    2.695  Skewness    1.751  Kurtosis    5.927
--------------------------------------------------------------------------------
( -Infinity,     0.2463)   |
[    0.2463,      2.451)   |###############################################-
[     2.451,      4.655)   |##################################################
[     4.655,      6.860)   |############-
[     6.860,      9.064)   |##=
[     9.064,      11.27)   |=
[     11.27,      13.47)   |-
[     13.47,      15.68)   |-
[     15.68,      17.88)   |-
[     17.88,      20.09)   |-
[     20.09,      22.29)   |-
[     22.29,      24.50)   |-
[     24.50,      26.70)   |-
[     26.70,      28.90)   |-
[     28.90,      31.11)   |-
[     31.11,      33.31)   |-
[     33.31,      35.52)   |-
[     35.52,      37.72)   |
[     37.72,      39.93)   |-
[     39.93,      42.13)   |
[     42.13,      44.34)   |
[     44.34,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing logistic distribution, m 1, s 0.5
Drawing 10000000 samples...

Expected: N 10000000  Mean    1.000  StdDev   0.9069  Variance   0.8225  Skewness    0.000  Kurtosis    1.200
Actual:   N 10000000  Mean    1.000  StdDev   0.9065  Variance   0.8218  Skewness 0.003453  Kurtosis    1.196
--------------------------------------------------------------------------------
( -Infinity,     -7.332)   |
[    -7.332,     -6.336)   |-
[    -6.336,     -5.340)   |-
[    -5.340,     -4.344)   |-
[    -4.344,     -3.347)   |-
[    -3.347,     -2.351)   |-
[    -2.351,     -1.355)   |=
[    -1.355,    -0.3584)   |#####=
[   -0.3584,     0.6379)   |#############################-
[    0.6379,      1.634)   |##################################################
[     1.634,      2.630)   |####################-
[     2.630,      3.627)   |###-
[     3.627,      4.623)   |-
[     4.623,      5.619)   |-
[     5.619,      6.616)   |-
[     6.616,      7.612)   |-
[     7.612,      8.608)   |-
[     8.608,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing cauchy distribution, m 1, s 0.5
Drawing 10000000 samples...

Expected: N 10000000  Mean    ---    StdDev    ---    Variance    ---    Skewness    ---    Kurtosis    ---  
Actual:   N 10000000  Mean  -0.6087  StdDev    6600.  Variance 4.355e+07  Skewness   -2630.  Kurtosis 8.166e+06
--------------------------------------------------------------------------------
( -Infinity, -1.980e+07)   |
[-1.980e+07, -1.851e+07)   |-
[-1.851e+07, -1.723e+07)   |
[-1.723e+07, -1.594e+07)   |
[-1.594e+07, -1.465e+07)   |
[-1.465e+07, -1.337e+07)   |
[-1.337e+07, -1.208e+07)   |
[-1.208e+07, -1.079e+07)   |
[-1.079e+07, -9.508e+06)   |
[-9.508e+06, -8.221e+06)   |
[-8.221e+06, -6.935e+06)   |
[-6.935e+06, -5.648e+06)   |
[-5.648e+06, -4.362e+06)   |
[-4.362e+06, -3.076e+06)   |
[-3.076e+06, -1.789e+06)   |
[-1.789e+06, -5.031e+05)   |-
[-5.031e+05,  7.833e+05)   |##################################################
[ 7.833e+05,  2.070e+06)   |
[ 2.070e+06,  3.356e+06)   |
[ 3.356e+06,  4.642e+06)   |
[ 4.642e+06,  5.929e+06)   |
[ 5.929e+06,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing beta distribution, shape 2, scale 5
Drawing 10000000 samples...

Expected: N 10000000  Mean   0.2857  StdDev   0.1597  Variance  0.02551  Skewness   0.5963  Kurtosis  -0.1200
Actual:   N 10000000  Mean   0.2856  StdDev   0.1597  Variance  0.02550  Skewness   0.5971  Kurtosis  -0.1180
--------------------------------------------------------------------------------
( -Infinity,  0.0001369)   |
[ 0.0001369,     0.9773)   |##################################################
[    0.9773,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing beta distribution, shape 2, scale 5, left 0, right 1
Drawing 10000000 samples...

Expected: N 10000000  Mean   0.2857  StdDev   0.1597  Variance  0.02551  Skewness   0.5963  Kurtosis  -0.1200
Actual:   N 10000000  Mean   0.2857  StdDev   0.1597  Variance  0.02550  Skewness   0.5955  Kurtosis  -0.1218
--------------------------------------------------------------------------------
( -Infinity,  9.697e-05)   |
[ 9.697e-05,     0.9818)   |##################################################
[    0.9818,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing beta distribution, shape 0.5, scale 2, left 0, right 1
Drawing 10000000 samples...

Expected: N 10000000  Mean   0.2000  StdDev   0.2138  Variance  0.04571  Skewness    1.247  Kurtosis   0.8182
Actual:   N 10000000  Mean   0.1999  StdDev   0.2139  Variance  0.04574  Skewness    1.247  Kurtosis   0.8174
--------------------------------------------------------------------------------
( -Infinity,  3.442e-20)   |
[ 3.442e-20,     0.9992)   |##################################################
[    0.9992,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing beta distribution, shape 0.5, scale 0.5, left 2, right 5
Drawing 10000000 samples...

Expected: N 10000000  Mean    3.500  StdDev    1.061  Variance    1.125  Skewness    0.000  Kurtosis   -1.500
Actual:   N 10000000  Mean    3.500  StdDev    1.061  Variance    1.126  Skewness 0.0008635  Kurtosis   -1.501
--------------------------------------------------------------------------------
( -Infinity,      2.000)   |
[     2.000,      3.000)   |##################################################
[     3.000,      4.000)   |###########################=
[     4.000,      5.000)   |#################################################=
[     5.000,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing PERT distribution, left 2, mode 5, right 10
Drawing 10000000 samples...

Expected: N 10000000  Mean    5.333  StdDev    1.491  Variance    2.222  Skewness   0.2236  Kurtosis  -0.6000
Actual:   N 10000000  Mean    5.334  StdDev    1.490  Variance    2.221  Skewness   0.2236  Kurtosis  -0.5984
--------------------------------------------------------------------------------
( -Infinity,      2.002)   |
[     2.002,      2.995)   |##########-
[     2.995,      3.989)   |##################################=
[     3.989,      4.982)   |#################################################-
[     4.982,      5.975)   |##################################################
[     5.975,      6.968)   |#######################################-
[     6.968,      7.961)   |#######################-
[     7.961,      8.955)   |########=
[     8.955,      9.948)   |#-
[     9.948,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing Pareto distribution, shape 3, scale 2
Drawing 10000000 samples...

Expected: N 10000000  Mean    3.000  StdDev    1.732  Variance    3.000  Skewness    ---    Kurtosis    ---  
Actual:   N 10000000  Mean    2.999  StdDev    1.724  Variance    2.973  Skewness    22.60  Kurtosis    4105.
--------------------------------------------------------------------------------
( -Infinity,      2.000)   |
[     2.000,      37.15)   |##################################################
[     37.15,      72.31)   |-
[     72.31,      107.5)   |-
[     107.5,      142.6)   |-
[     142.6,      177.8)   |-
[     177.8,      212.9)   |-
[     212.9,      248.1)   |-
[     248.1,      283.2)   |-
[     283.2,      318.4)   |-
[     318.4,      353.5)   |
[     353.5,      388.7)   |
[     388.7,      423.8)   |
[     423.8,      459.0)   |-
[     459.0,      494.2)   |
[     494.2,      529.3)   |
[     529.3,      564.5)   |
[     564.5,      599.6)   |
[     599.6,      634.8)   |
[     634.8,      669.9)   |
[     669.9,      705.1)   |
[     705.1,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing chisquare distribution, v 4
Drawing 10000000 samples...

Expected: N 10000000  Mean    4.000  StdDev    2.828  Variance    8.000  Skewness    1.414  Kurtosis    3.000
Actual:   N 10000000  Mean    4.000  StdDev    2.827  Variance    7.990  Skewness    1.412  Kurtosis    2.984
--------------------------------------------------------------------------------
( -Infinity,  6.448e-05)   |
[ 6.448e-05,      1.865)   |#####################################=
[     1.865,      3.731)   |##################################################
[     3.731,      5.596)   |#################################=
[     5.596,      7.461)   |##################=
[     7.461,      9.326)   |#########-
[     9.326,      11.19)   |####=
[     11.19,      13.06)   |##-
[     13.06,      14.92)   |=
[     14.92,      16.79)   |-
[     16.79,      18.65)   |-
[     18.65,      20.52)   |-
[     20.52,      22.38)   |-
[     22.38,      24.25)   |-
[     24.25,      26.11)   |-
[     26.11,      27.98)   |-
[     27.98,      29.84)   |-
[     29.84,      31.71)   |-
[     31.71,      33.57)   |-
[     33.57,      35.44)   |-
[     35.44,      37.30)   |-
[     37.30,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing f distribution, a 3, b 5
Drawing 10000000 samples...

Expected: N 10000000  Mean    1.667  StdDev    3.333  Variance    11.11  Skewness    ---    Kurtosis    ---  
Actual:   N 10000000  Mean    1.667  StdDev    3.553  Variance    12.62  Skewness    230.0  Kurtosis 2.342e+05
--------------------------------------------------------------------------------
( -Infinity,  1.324e-06)   |
[ 1.324e-06,      215.8)   |##################################################
[     215.8,      431.6)   |-
[     431.6,      647.4)   |-
[     647.4,      863.3)   |-
[     863.3,      1079.)   |-
[     1079.,      1295.)   |
[     1295.,      1511.)   |-
[     1511.,      1727.)   |
[     1727.,      1942.)   |
[     1942.,      2158.)   |-
[     2158.,      2374.)   |
[     2374.,      2590.)   |
[     2590.,      2806.)   |
[     2806.,      3021.)   |
[     3021.,      3237.)   |
[     3237.,      3453.)   |
[     3453.,      3669.)   |
[     3669.,      3885.)   |
[     3885.,      4100.)   |
[     4100.,      4316.)   |
[     4316.,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing Student's t distribution, v 3
Drawing 10000000 samples...

Expected: N 10000000  Mean    0.000  StdDev    1.732  Variance    3.000  Skewness    ---    Kurtosis    ---  
Actual:   N 10000000  Mean -0.0002842  StdDev    1.732  Variance    3.001  Skewness   -1.171  Kurtosis    480.1
--------------------------------------------------------------------------------
( -Infinity,     -378.7)   |
[    -378.7,     -345.9)   |-
[    -345.9,     -313.0)   |
[    -313.0,     -280.2)   |
[    -280.2,     -247.3)   |
[    -247.3,     -214.5)   |
[    -214.5,     -181.7)   |-
[    -181.7,     -148.8)   |-
[    -148.8,     -116.0)   |-
[    -116.0,     -83.13)   |-
[    -83.13,     -50.28)   |-
[    -50.28,     -17.44)   |-
[    -17.44,      15.41)   |##################################################
[     15.41,      48.25)   |-
[     48.25,      81.10)   |-
[     81.10,      113.9)   |-
[     113.9,      146.8)   |-
[     146.8,      179.6)   |-
[     179.6,      212.5)   |
[     212.5,      245.3)   |-
[     245.3,      278.2)   |
[     278.2,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing t distribution, m 1, s 2, v 3,
Drawing 10000000 samples...

Expected: N 10000000  Mean    1.000  StdDev    3.464  Variance    12.00  Skewness    ---    Kurtosis    ---  
Actual:   N 10000000  Mean   0.9989  StdDev    3.461  Variance    11.98  Skewness   -1.110  Kurtosis    506.1
--------------------------------------------------------------------------------
( -Infinity,     -804.9)   |
[    -804.9,     -736.0)   |-
[    -736.0,     -667.1)   |
[    -667.1,     -598.3)   |
[    -598.3,     -529.4)   |
[    -529.4,     -460.5)   |
[    -460.5,     -391.7)   |
[    -391.7,     -322.8)   |-
[    -322.8,     -253.9)   |-
[    -253.9,     -185.1)   |-
[    -185.1,     -116.2)   |-
[    -116.2,     -47.35)   |-
[    -47.35,      21.52)   |##################################################
[     21.52,      90.38)   |-
[     90.38,      159.2)   |-
[     159.2,      228.1)   |-
[     228.1,      297.0)   |-
[     297.0,      365.8)   |
[     365.8,      434.7)   |
[     434.7,      503.6)   |
[     503.6,      572.4)   |
[     572.4,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing Rayleigh distribution, s 1.5
Drawing 10000000 samples...

Expected: N 10000000  Mean    1.880  StdDev   0.9827  Variance   0.9657  Skewness   0.6311  Kurtosis   0.2451
Actual:   N 10000000  Mean    1.881  StdDev   0.9827  Variance   0.9658  Skewness   0.6315  Kurtosis   0.2465
--------------------------------------------------------------------------------
( -Infinity,  0.0003147)   |
[ 0.0003147,     0.9742)   |#########################-
[    0.9742,      1.948)   |##################################################
[     1.948,      2.922)   |####################################=
[     2.922,      3.896)   |###############-
[     3.896,      4.870)   |###=
[     4.870,      5.844)   |=
[     5.844,      6.818)   |-
[     6.818,      7.792)   |-
[     7.792,      8.765)   |-
[     8.765,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================
************************* Integer-valued distributions *************************

Quality testing unbiased coin flip, p = 0.5
Drawing 10000000 samples...

Expected: N 10000000  Mean   0.5000  StdDev   0.5000  Variance   0.2500  Skewness    0.000  Kurtosis   -2.000
Actual:   N 10000000  Mean   0.4998  StdDev   0.5000  Variance   0.2500  Skewness 0.0007756  Kurtosis   -2.000
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      1.000)   |##################################################
[     1.000,  Infinity )   |#################################################=
--------------------------------------------------------------------------------
================================================================================

Quality testing biased Bernoulli trials, p = 0.6
Drawing 10000000 samples...

Expected: N 10000000  Mean   0.6000  StdDev   0.4899  Variance   0.2400  Skewness  -0.4082  Kurtosis   -1.833
Actual:   N 10000000  Mean   0.5999  StdDev   0.4899  Variance   0.2400  Skewness  -0.4080  Kurtosis   -1.834
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      1.000)   |#################################-
[     1.000,  Infinity )   |##################################################
--------------------------------------------------------------------------------
================================================================================

Quality testing geometric distribution, p = 0.1
Drawing 10000000 samples...

Expected: N 10000000  Mean    10.00  StdDev    9.487  Variance    90.00  Skewness    2.667  Kurtosis    5.111
Actual:   N 10000000  Mean    10.00  StdDev    9.491  Variance    90.08  Skewness    2.004  Kurtosis    6.020
--------------------------------------------------------------------------------
( -Infinity,      1.000)   |
[     1.000,      8.350)   |##################################################
[     8.350,      15.70)   |###################=
[     15.70,      23.05)   |##########-
[     23.05,      30.40)   |####-
[     30.40,      37.75)   |#=
[     37.75,      45.10)   |#-
[     45.10,      52.45)   |-
[     52.45,      59.80)   |-
[     59.80,      67.15)   |-
[     67.15,      74.50)   |-
[     74.50,      81.85)   |-
[     81.85,      89.20)   |-
[     89.20,      96.55)   |-
[     96.55,      103.9)   |-
[     103.9,      111.2)   |-
[     111.2,      118.6)   |-
[     118.6,      125.9)   |-
[     125.9,      133.3)   |-
[     133.3,      140.7)   |-
[     140.7,      148.0)   |-
[     148.0,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing binomial distribution, n = 10, p = 0.1
Drawing 10000000 samples...

Expected: N 10000000  Mean    1.000  StdDev   0.9487  Variance   0.9000  Skewness   0.8433  Kurtosis   0.5111
Actual:   N 10000000  Mean    1.000  StdDev   0.9489  Variance   0.9004  Skewness   0.8440  Kurtosis   0.5146
--------------------------------------------------------------------------------
( -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,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing negative binomial (Pascal) distribution, m = 10, p = 0.1
Drawing 10000000 samples...

Expected: N 10000000  Mean    90.00  StdDev    30.00  Variance    900.0  Skewness   0.6333  Kurtosis   0.6011
Actual:   N 10000000  Mean    90.01  StdDev    30.01  Variance    900.7  Skewness   0.6336  Kurtosis   0.5996
--------------------------------------------------------------------------------
( -Infinity,      6.000)   |
[     6.000,      21.45)   |-
[     21.45,      36.90)   |###-
[     36.90,      52.35)   |################=
[     52.35,      67.80)   |###################################-
[     67.80,      83.25)   |##################################################
[     83.25,      98.70)   |#############################################-
[     98.70,      114.1)   |####################################-
[     114.1,      129.6)   |#####################=
[     129.6,      145.0)   |############=
[     145.0,      160.5)   |#####=
[     160.5,      175.9)   |##=
[     175.9,      191.4)   |#-
[     191.4,      206.8)   |-
[     206.8,      222.3)   |-
[     222.3,      237.8)   |-
[     237.8,      253.2)   |-
[     253.2,      268.6)   |-
[     268.6,      284.1)   |-
[     284.1,      299.6)   |-
[     299.6,      315.0)   |-
[     315.0,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing Poisson distribution, r = 10
Drawing 10000000 samples...

Expected: N 10000000  Mean    10.00  StdDev    3.162  Variance    10.00  Skewness   0.3162  Kurtosis   0.1000
Actual:   N 10000000  Mean    9.999  StdDev    3.163  Variance    10.01  Skewness   0.3162  Kurtosis   0.1004
--------------------------------------------------------------------------------
( -Infinity,      0.000)   |
[     0.000,      1.500)   |-
[     1.500,      3.000)   |-
[     3.000,      4.500)   |#####-
[     4.500,      6.000)   |#######=
[     6.000,      7.500)   |##############################=
[     7.500,      9.000)   |######################=
[     9.000,      10.50)   |##################################################
[     10.50,      12.00)   |######################=
[     12.00,      13.50)   |#################################=
[     13.50,      15.00)   |##########-
[     15.00,      16.50)   |###########-
[     16.50,      18.00)   |##=
[     18.00,      19.50)   |##-
[     19.50,      21.00)   |-
[     21.00,      22.50)   |-
[     22.50,      24.00)   |-
[     24.00,      25.50)   |-
[     25.50,      27.00)   |-
[     27.00,      28.50)   |-
[     28.50,      30.00)   |-
[     30.00,  Infinity )   |-
--------------------------------------------------------------------------------
================================================================================

Quality testing dice (discrete uniform) distribution, a = 1, b = 6
Drawing 10000000 samples...

Expected: N 10000000  Mean    3.500  StdDev    1.708  Variance    2.917  Skewness    0.000  Kurtosis   -1.269
Actual:   N 10000000  Mean    3.500  StdDev    1.708  Variance    2.917  Skewness 0.0001693  Kurtosis   -1.269
--------------------------------------------------------------------------------
( -Infinity,      1.000)   |
[     1.000,      2.000)   |#################################################=
[     2.000,      3.000)   |##################################################
[     3.000,      4.000)   |#################################################=
[     4.000,      5.000)   |#################################################=
[     5.000,      6.000)   |#################################################=
[     6.000,  Infinity )   |#################################################=
--------------------------------------------------------------------------------
================================================================================

Quality testing loaded dice distribution, n = 7
Drawing 10000000 samples...

Expected: N 10000000  Mean    4.150  StdDev    1.768  Variance    3.127  Skewness  -0.7704  Kurtosis  -0.3742
Actual:   N 10000000  Mean    4.149  StdDev    1.769  Variance    3.129  Skewness  -0.7702  Kurtosis  -0.3752
--------------------------------------------------------------------------------
( -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,  Infinity )   |##################################################
--------------------------------------------------------------------------------
================================================================================

Quality testing vose alias sampling, n = 7
Drawing 10000000 samples...

Expected: N 10000000  Mean    4.150  StdDev    1.768  Variance    3.127  Skewness  -0.7704  Kurtosis  -0.3742
Actual:   N 10000000  Mean    4.150  StdDev    1.769  Variance    3.129  Skewness  -0.7704  Kurtosis  -0.3746
--------------------------------------------------------------------------------
( -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,  Infinity )   |##################################################
--------------------------------------------------------------------------------
================================================================================
********************************************************************************
