1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
|
"""
==========================================
Statistical functions (:mod:`scipy.stats`)
==========================================
.. module:: scipy.stats
This module contains a large number of probability distributions as
well as a growing library of statistical functions.
Each univariate distribution is an instance of a subclass of `rv_continuous`
(`rv_discrete` for discrete distributions):
.. autosummary::
:toctree: generated/
rv_continuous
rv_discrete
Continuous distributions
========================
.. autosummary::
:toctree: generated/
alpha -- Alpha
anglit -- Anglit
arcsine -- Arcsine
beta -- Beta
betaprime -- Beta Prime
bradford -- Bradford
burr -- Burr (Type III)
burr12 -- Burr (Type XII)
cauchy -- Cauchy
chi -- Chi
chi2 -- Chi-squared
cosine -- Cosine
dgamma -- Double Gamma
dweibull -- Double Weibull
erlang -- Erlang
expon -- Exponential
exponnorm -- Exponentially Modified Normal
exponweib -- Exponentiated Weibull
exponpow -- Exponential Power
f -- F (Snecdor F)
fatiguelife -- Fatigue Life (Birnbaum-Saunders)
fisk -- Fisk
foldcauchy -- Folded Cauchy
foldnorm -- Folded Normal
frechet_r -- Frechet Right Sided, Extreme Value Type II (Extreme LB) or weibull_min
frechet_l -- Frechet Left Sided, Weibull_max
genlogistic -- Generalized Logistic
gennorm -- Generalized normal
genpareto -- Generalized Pareto
genexpon -- Generalized Exponential
genextreme -- Generalized Extreme Value
gausshyper -- Gauss Hypergeometric
gamma -- Gamma
gengamma -- Generalized gamma
genhalflogistic -- Generalized Half Logistic
gilbrat -- Gilbrat
gompertz -- Gompertz (Truncated Gumbel)
gumbel_r -- Right Sided Gumbel, Log-Weibull, Fisher-Tippett, Extreme Value Type I
gumbel_l -- Left Sided Gumbel, etc.
halfcauchy -- Half Cauchy
halflogistic -- Half Logistic
halfnorm -- Half Normal
halfgennorm -- Generalized Half Normal
hypsecant -- Hyperbolic Secant
invgamma -- Inverse Gamma
invgauss -- Inverse Gaussian
invweibull -- Inverse Weibull
johnsonsb -- Johnson SB
johnsonsu -- Johnson SU
kappa4 -- Kappa 4 parameter
kappa3 -- Kappa 3 parameter
ksone -- Kolmogorov-Smirnov one-sided (no stats)
kstwobign -- Kolmogorov-Smirnov two-sided test for Large N (no stats)
laplace -- Laplace
levy -- Levy
levy_l
levy_stable
logistic -- Logistic
loggamma -- Log-Gamma
loglaplace -- Log-Laplace (Log Double Exponential)
lognorm -- Log-Normal
lomax -- Lomax (Pareto of the second kind)
maxwell -- Maxwell
mielke -- Mielke's Beta-Kappa
nakagami -- Nakagami
ncx2 -- Non-central chi-squared
ncf -- Non-central F
nct -- Non-central Student's T
norm -- Normal (Gaussian)
pareto -- Pareto
pearson3 -- Pearson type III
powerlaw -- Power-function
powerlognorm -- Power log normal
powernorm -- Power normal
rdist -- R-distribution
reciprocal -- Reciprocal
rayleigh -- Rayleigh
rice -- Rice
recipinvgauss -- Reciprocal Inverse Gaussian
semicircular -- Semicircular
skewnorm -- Skew normal
t -- Student's T
trapz -- Trapezoidal
triang -- Triangular
truncexpon -- Truncated Exponential
truncnorm -- Truncated Normal
tukeylambda -- Tukey-Lambda
uniform -- Uniform
vonmises -- Von-Mises (Circular)
vonmises_line -- Von-Mises (Line)
wald -- Wald
weibull_min -- Minimum Weibull (see Frechet)
weibull_max -- Maximum Weibull (see Frechet)
wrapcauchy -- Wrapped Cauchy
Multivariate distributions
==========================
.. autosummary::
:toctree: generated/
multivariate_normal -- Multivariate normal distribution
matrix_normal -- Matrix normal distribution
dirichlet -- Dirichlet
wishart -- Wishart
invwishart -- Inverse Wishart
special_ortho_group -- SO(N) group
ortho_group -- O(N) group
random_correlation -- random correlation matrices
Discrete distributions
======================
.. autosummary::
:toctree: generated/
bernoulli -- Bernoulli
binom -- Binomial
boltzmann -- Boltzmann (Truncated Discrete Exponential)
dlaplace -- Discrete Laplacian
geom -- Geometric
hypergeom -- Hypergeometric
logser -- Logarithmic (Log-Series, Series)
nbinom -- Negative Binomial
planck -- Planck (Discrete Exponential)
poisson -- Poisson
randint -- Discrete Uniform
skellam -- Skellam
zipf -- Zipf
Statistical functions
=====================
Several of these functions have a similar version in scipy.stats.mstats
which work for masked arrays.
.. autosummary::
:toctree: generated/
describe -- Descriptive statistics
gmean -- Geometric mean
hmean -- Harmonic mean
kurtosis -- Fisher or Pearson kurtosis
kurtosistest --
mode -- Modal value
moment -- Central moment
normaltest --
skew -- Skewness
skewtest --
kstat --
kstatvar --
tmean -- Truncated arithmetic mean
tvar -- Truncated variance
tmin --
tmax --
tstd --
tsem --
variation -- Coefficient of variation
find_repeats
trim_mean
.. autosummary::
:toctree: generated/
cumfreq
histogram2
histogram
itemfreq
percentileofscore
scoreatpercentile
relfreq
.. autosummary::
:toctree: generated/
binned_statistic -- Compute a binned statistic for a set of data.
binned_statistic_2d -- Compute a 2-D binned statistic for a set of data.
binned_statistic_dd -- Compute a d-D binned statistic for a set of data.
.. autosummary::
:toctree: generated/
obrientransform
signaltonoise
bayes_mvs
mvsdist
sem
zmap
zscore
iqr
.. autosummary::
:toctree: generated/
sigmaclip
threshold
trimboth
trim1
.. autosummary::
:toctree: generated/
f_oneway
pearsonr
spearmanr
pointbiserialr
kendalltau
linregress
theilslopes
f_value
.. autosummary::
:toctree: generated/
ttest_1samp
ttest_ind
ttest_ind_from_stats
ttest_rel
kstest
chisquare
power_divergence
ks_2samp
mannwhitneyu
tiecorrect
rankdata
ranksums
wilcoxon
kruskal
friedmanchisquare
combine_pvalues
ss
square_of_sums
jarque_bera
.. autosummary::
:toctree: generated/
ansari
bartlett
levene
shapiro
anderson
anderson_ksamp
binom_test
fligner
median_test
mood
.. autosummary::
:toctree: generated/
boxcox
boxcox_normmax
boxcox_llf
entropy
.. autosummary::
:toctree: generated/
chisqprob
betai
Circular statistical functions
==============================
.. autosummary::
:toctree: generated/
circmean
circvar
circstd
Contingency table functions
===========================
.. autosummary::
:toctree: generated/
chi2_contingency
contingency.expected_freq
contingency.margins
fisher_exact
Plot-tests
==========
.. autosummary::
:toctree: generated/
ppcc_max
ppcc_plot
probplot
boxcox_normplot
Masked statistics functions
===========================
.. toctree::
stats.mstats
Univariate and multivariate kernel density estimation (:mod:`scipy.stats.kde`)
==============================================================================
.. autosummary::
:toctree: generated/
gaussian_kde
For many more stat related functions install the software R and the
interface package rpy.
"""
from __future__ import division, print_function, absolute_import
from .stats import *
from .distributions import *
from .morestats import *
from ._binned_statistic import *
from .kde import gaussian_kde
from . import mstats
from .contingency import chi2_contingency
from ._multivariate import *
__all__ = [s for s in dir() if not s.startswith("_")] # Remove dunders.
from numpy.testing import Tester
test = Tester().test
|
