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1"""
2.. _statsrefmanual:
4==========================================
5Statistical functions (:mod:`scipy.stats`)
6==========================================
8.. currentmodule:: scipy.stats
10This module contains a large number of probability distributions as
11well as a growing library of statistical functions.
13Each univariate distribution is an instance of a subclass of `rv_continuous`
14(`rv_discrete` for discrete distributions):
16.. autosummary::
17 :toctree: generated/
19 rv_continuous
20 rv_discrete
21 rv_histogram
23Continuous distributions
24========================
26.. autosummary::
27 :toctree: generated/
29 alpha -- Alpha
30 anglit -- Anglit
31 arcsine -- Arcsine
32 argus -- Argus
33 beta -- Beta
34 betaprime -- Beta Prime
35 bradford -- Bradford
36 burr -- Burr (Type III)
37 burr12 -- Burr (Type XII)
38 cauchy -- Cauchy
39 chi -- Chi
40 chi2 -- Chi-squared
41 cosine -- Cosine
42 crystalball -- Crystalball
43 dgamma -- Double Gamma
44 dweibull -- Double Weibull
45 erlang -- Erlang
46 expon -- Exponential
47 exponnorm -- Exponentially Modified Normal
48 exponweib -- Exponentiated Weibull
49 exponpow -- Exponential Power
50 f -- F (Snecdor F)
51 fatiguelife -- Fatigue Life (Birnbaum-Saunders)
52 fisk -- Fisk
53 foldcauchy -- Folded Cauchy
54 foldnorm -- Folded Normal
55 frechet_r -- Deprecated. Alias for weibull_min
56 frechet_l -- Deprecated. Alias for weibull_max
57 genlogistic -- Generalized Logistic
58 gennorm -- Generalized normal
59 genpareto -- Generalized Pareto
60 genexpon -- Generalized Exponential
61 genextreme -- Generalized Extreme Value
62 gausshyper -- Gauss Hypergeometric
63 gamma -- Gamma
64 gengamma -- Generalized gamma
65 genhalflogistic -- Generalized Half Logistic
66 geninvgauss -- Generalized Inverse Gaussian
67 gilbrat -- Gilbrat
68 gompertz -- Gompertz (Truncated Gumbel)
69 gumbel_r -- Right Sided Gumbel, Log-Weibull, Fisher-Tippett, Extreme Value Type I
70 gumbel_l -- Left Sided Gumbel, etc.
71 halfcauchy -- Half Cauchy
72 halflogistic -- Half Logistic
73 halfnorm -- Half Normal
74 halfgennorm -- Generalized Half Normal
75 hypsecant -- Hyperbolic Secant
76 invgamma -- Inverse Gamma
77 invgauss -- Inverse Gaussian
78 invweibull -- Inverse Weibull
79 johnsonsb -- Johnson SB
80 johnsonsu -- Johnson SU
81 kappa4 -- Kappa 4 parameter
82 kappa3 -- Kappa 3 parameter
83 ksone -- Distribution of Kolmogorov-Smirnov one-sided test statistic
84 kstwo -- Distribution of Kolmogorov-Smirnov two-sided test statistic
85 kstwobign -- Limiting Distribution of scaled Kolmogorov-Smirnov two-sided test statistic.
86 laplace -- Laplace
87 levy -- Levy
88 levy_l
89 levy_stable
90 logistic -- Logistic
91 loggamma -- Log-Gamma
92 loglaplace -- Log-Laplace (Log Double Exponential)
93 lognorm -- Log-Normal
94 loguniform -- Log-Uniform
95 lomax -- Lomax (Pareto of the second kind)
96 maxwell -- Maxwell
97 mielke -- Mielke's Beta-Kappa
98 moyal -- Moyal
99 nakagami -- Nakagami
100 ncx2 -- Non-central chi-squared
101 ncf -- Non-central F
102 nct -- Non-central Student's T
103 norm -- Normal (Gaussian)
104 norminvgauss -- Normal Inverse Gaussian
105 pareto -- Pareto
106 pearson3 -- Pearson type III
107 powerlaw -- Power-function
108 powerlognorm -- Power log normal
109 powernorm -- Power normal
110 rdist -- R-distribution
111 rayleigh -- Rayleigh
112 rice -- Rice
113 recipinvgauss -- Reciprocal Inverse Gaussian
114 semicircular -- Semicircular
115 skewnorm -- Skew normal
116 t -- Student's T
117 trapz -- Trapezoidal
118 triang -- Triangular
119 truncexpon -- Truncated Exponential
120 truncnorm -- Truncated Normal
121 tukeylambda -- Tukey-Lambda
122 uniform -- Uniform
123 vonmises -- Von-Mises (Circular)
124 vonmises_line -- Von-Mises (Line)
125 wald -- Wald
126 weibull_min -- Minimum Weibull (see Frechet)
127 weibull_max -- Maximum Weibull (see Frechet)
128 wrapcauchy -- Wrapped Cauchy
130Multivariate distributions
131==========================
133.. autosummary::
134 :toctree: generated/
136 multivariate_normal -- Multivariate normal distribution
137 matrix_normal -- Matrix normal distribution
138 dirichlet -- Dirichlet
139 wishart -- Wishart
140 invwishart -- Inverse Wishart
141 multinomial -- Multinomial distribution
142 special_ortho_group -- SO(N) group
143 ortho_group -- O(N) group
144 unitary_group -- U(N) group
145 random_correlation -- random correlation matrices
147Discrete distributions
148======================
150.. autosummary::
151 :toctree: generated/
153 bernoulli -- Bernoulli
154 betabinom -- Beta-Binomial
155 binom -- Binomial
156 boltzmann -- Boltzmann (Truncated Discrete Exponential)
157 dlaplace -- Discrete Laplacian
158 geom -- Geometric
159 hypergeom -- Hypergeometric
160 logser -- Logarithmic (Log-Series, Series)
161 nbinom -- Negative Binomial
162 planck -- Planck (Discrete Exponential)
163 poisson -- Poisson
164 randint -- Discrete Uniform
165 skellam -- Skellam
166 zipf -- Zipf
167 yulesimon -- Yule-Simon
169An overview of statistical functions is given below.
170Several of these functions have a similar version in
171`scipy.stats.mstats` which work for masked arrays.
173Summary statistics
174==================
176.. autosummary::
177 :toctree: generated/
179 describe -- Descriptive statistics
180 gmean -- Geometric mean
181 hmean -- Harmonic mean
182 kurtosis -- Fisher or Pearson kurtosis
183 mode -- Modal value
184 moment -- Central moment
185 skew -- Skewness
186 kstat --
187 kstatvar --
188 tmean -- Truncated arithmetic mean
189 tvar -- Truncated variance
190 tmin --
191 tmax --
192 tstd --
193 tsem --
194 variation -- Coefficient of variation
195 find_repeats
196 trim_mean
197 gstd -- Geometric Standard Deviation
198 iqr
199 sem
200 bayes_mvs
201 mvsdist
202 entropy
203 median_absolute_deviation
204 median_abs_deviation
206Frequency statistics
207====================
209.. autosummary::
210 :toctree: generated/
212 cumfreq
213 itemfreq
214 percentileofscore
215 scoreatpercentile
216 relfreq
218.. autosummary::
219 :toctree: generated/
221 binned_statistic -- Compute a binned statistic for a set of data.
222 binned_statistic_2d -- Compute a 2-D binned statistic for a set of data.
223 binned_statistic_dd -- Compute a d-D binned statistic for a set of data.
225Correlation functions
226=====================
228.. autosummary::
229 :toctree: generated/
231 f_oneway
232 pearsonr
233 spearmanr
234 pointbiserialr
235 kendalltau
236 weightedtau
237 linregress
238 siegelslopes
239 theilslopes
240 multiscale_graphcorr
242Statistical tests
243=================
245.. autosummary::
246 :toctree: generated/
248 ttest_1samp
249 ttest_ind
250 ttest_ind_from_stats
251 ttest_rel
252 chisquare
253 power_divergence
254 kstest
255 ks_1samp
256 ks_2samp
257 epps_singleton_2samp
258 mannwhitneyu
259 tiecorrect
260 rankdata
261 ranksums
262 wilcoxon
263 kruskal
264 friedmanchisquare
265 brunnermunzel
266 combine_pvalues
267 jarque_bera
269.. autosummary::
270 :toctree: generated/
272 ansari
273 bartlett
274 levene
275 shapiro
276 anderson
277 anderson_ksamp
278 binom_test
279 fligner
280 median_test
281 mood
282 skewtest
283 kurtosistest
284 normaltest
286Transformations
287===============
289.. autosummary::
290 :toctree: generated/
292 boxcox
293 boxcox_normmax
294 boxcox_llf
295 yeojohnson
296 yeojohnson_normmax
297 yeojohnson_llf
298 obrientransform
299 sigmaclip
300 trimboth
301 trim1
302 zmap
303 zscore
305Statistical distances
306=====================
308.. autosummary::
309 :toctree: generated/
311 wasserstein_distance
312 energy_distance
314Random variate generation
315=========================
317.. autosummary::
318 :toctree: generated/
320 rvs_ratio_uniforms
322Circular statistical functions
323==============================
325.. autosummary::
326 :toctree: generated/
328 circmean
329 circvar
330 circstd
332Contingency table functions
333===========================
335.. autosummary::
336 :toctree: generated/
338 chi2_contingency
339 contingency.expected_freq
340 contingency.margins
341 fisher_exact
343Plot-tests
344==========
346.. autosummary::
347 :toctree: generated/
349 ppcc_max
350 ppcc_plot
351 probplot
352 boxcox_normplot
353 yeojohnson_normplot
356Masked statistics functions
357===========================
359.. toctree::
361 stats.mstats
364Univariate and multivariate kernel density estimation
365=====================================================
367.. autosummary::
368 :toctree: generated/
370 gaussian_kde
372Warnings used in :mod:`scipy.stats`
373===================================
375.. autosummary::
376 :toctree: generated/
378 F_onewayConstantInputWarning
379 F_onewayBadInputSizesWarning
380 PearsonRConstantInputWarning
381 PearsonRNearConstantInputWarning
382 SpearmanRConstantInputWarning
384For many more stat related functions install the software R and the
385interface package rpy.
387"""
388from .stats import *
389from .distributions import *
390from .morestats import *
391from ._binned_statistic import *
392from .kde import gaussian_kde
393from . import mstats
394from .contingency import chi2_contingency
395from ._multivariate import *
397__all__ = [s for s in dir() if not s.startswith("_")] # Remove dunders.
399from scipy._lib._testutils import PytestTester
400test = PytestTester(__name__)
401del PytestTester