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"""
.. _statsrefmanual:
==========================================
Statistical functions (:mod:`scipy.stats`)
==========================================
.. currentmodule:: scipy.stats
This module contains a large number of probability distributions,
summary and frequency statistics, correlation functions and statistical
tests, masked statistics, kernel density estimation, quasi-Monte Carlo
functionality, and more.
Statistics is a very large area, and there are topics that are out of scope
for SciPy and are covered by other packages. Some of the most important ones
are:
- `statsmodels <https://www.statsmodels.org/stable/index.html>`__:
regression, linear models, time series analysis, extensions to topics
also covered by ``scipy.stats``.
- `Pandas <https://pandas.pydata.org/>`__: tabular data, time series
functionality, interfaces to other statistical languages.
- `PyMC <https://docs.pymc.io/>`__: Bayesian statistical
modeling, probabilistic machine learning.
- `scikit-learn <https://scikit-learn.org/>`__: classification, regression,
model selection.
- `Seaborn <https://seaborn.pydata.org/>`__: statistical data visualization.
- `rpy2 <https://rpy2.github.io/>`__: Python to R bridge.
Probability distributions
=========================
Each univariate distribution is an instance of a subclass of `rv_continuous`
(`rv_discrete` for discrete distributions):
.. autosummary::
:toctree: generated/
rv_continuous
rv_discrete
rv_histogram
Continuous distributions
------------------------
.. autosummary::
:toctree: generated/
alpha -- Alpha
anglit -- Anglit
arcsine -- Arcsine
argus -- Argus
beta -- Beta
betaprime -- Beta Prime
bradford -- Bradford
burr -- Burr (Type III)
burr12 -- Burr (Type XII)
cauchy -- Cauchy
chi -- Chi
chi2 -- Chi-squared
cosine -- Cosine
crystalball -- Crystalball
dgamma -- Double Gamma
dpareto_lognorm -- Double Pareto Lognormal
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
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
genhyperbolic -- Generalized Hyperbolic
geninvgauss -- Generalized Inverse Gaussian
gibrat -- Gibrat
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
irwinhall -- Irwin-Hall
jf_skew_t -- Jones and Faddy Skew-T
johnsonsb -- Johnson SB
johnsonsu -- Johnson SU
kappa4 -- Kappa 4 parameter
kappa3 -- Kappa 3 parameter
ksone -- Distribution of Kolmogorov-Smirnov one-sided test statistic
kstwo -- Distribution of Kolmogorov-Smirnov two-sided test statistic
kstwobign -- Limiting Distribution of scaled Kolmogorov-Smirnov two-sided test statistic.
landau -- Landau
laplace -- Laplace
laplace_asymmetric -- Asymmetric Laplace
levy -- Levy
levy_l
levy_stable
logistic -- Logistic
loggamma -- Log-Gamma
loglaplace -- Log-Laplace (Log Double Exponential)
lognorm -- Log-Normal
loguniform -- Log-Uniform
lomax -- Lomax (Pareto of the second kind)
maxwell -- Maxwell
mielke -- Mielke's Beta-Kappa
moyal -- Moyal
nakagami -- Nakagami
ncx2 -- Non-central chi-squared
ncf -- Non-central F
nct -- Non-central Student's T
norm -- Normal (Gaussian)
norminvgauss -- Normal Inverse Gaussian
pareto -- Pareto
pearson3 -- Pearson type III
powerlaw -- Power-function
powerlognorm -- Power log normal
powernorm -- Power normal
rdist -- R-distribution
rayleigh -- Rayleigh
rel_breitwigner -- Relativistic Breit-Wigner
rice -- Rice
recipinvgauss -- Reciprocal Inverse Gaussian
semicircular -- Semicircular
skewcauchy -- Skew Cauchy
skewnorm -- Skew normal
studentized_range -- Studentized Range
t -- Student's T
trapezoid -- Trapezoidal
triang -- Triangular
truncexpon -- Truncated Exponential
truncnorm -- Truncated Normal
truncpareto -- Truncated Pareto
truncweibull_min -- Truncated minimum Weibull distribution
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
The ``fit`` method of the univariate continuous distributions uses
maximum likelihood estimation to fit the distribution to a data set.
The ``fit`` method can accept regular data or *censored data*.
Censored data is represented with instances of the `CensoredData`
class.
.. autosummary::
:toctree: generated/
CensoredData
Multivariate distributions
--------------------------
.. autosummary::
:toctree: generated/
multivariate_normal -- Multivariate normal distribution
matrix_normal -- Matrix normal distribution
dirichlet -- Dirichlet
dirichlet_multinomial -- Dirichlet multinomial distribution
wishart -- Wishart
invwishart -- Inverse Wishart
multinomial -- Multinomial distribution
special_ortho_group -- SO(N) group
ortho_group -- O(N) group
unitary_group -- U(N) group
random_correlation -- random correlation matrices
multivariate_t -- Multivariate t-distribution
multivariate_hypergeom -- Multivariate hypergeometric distribution
normal_inverse_gamma -- Normal-inverse-gamma distribution
random_table -- Distribution of random tables with given marginals
uniform_direction -- Uniform distribution on S(N-1)
vonmises_fisher -- Von Mises-Fisher distribution
`scipy.stats.multivariate_normal` methods accept instances
of the following class to represent the covariance.
.. autosummary::
:toctree: generated/
Covariance -- Representation of a covariance matrix
Discrete distributions
----------------------
.. autosummary::
:toctree: generated/
bernoulli -- Bernoulli
betabinom -- Beta-Binomial
betanbinom -- Beta-Negative Binomial
binom -- Binomial
boltzmann -- Boltzmann (Truncated Discrete Exponential)
dlaplace -- Discrete Laplacian
geom -- Geometric
hypergeom -- Hypergeometric
logser -- Logarithmic (Log-Series, Series)
nbinom -- Negative Binomial
nchypergeom_fisher -- Fisher's Noncentral Hypergeometric
nchypergeom_wallenius -- Wallenius's Noncentral Hypergeometric
nhypergeom -- Negative Hypergeometric
planck -- Planck (Discrete Exponential)
poisson -- Poisson
poisson_binom -- Poisson Binomial
randint -- Discrete Uniform
skellam -- Skellam
yulesimon -- Yule-Simon
zipf -- Zipf (Zeta)
zipfian -- Zipfian
An overview of statistical functions is given below. Many of these functions
have a similar version in `scipy.stats.mstats` which work for masked arrays.
Summary statistics
==================
.. autosummary::
:toctree: generated/
describe -- Descriptive statistics
gmean -- Geometric mean
hmean -- Harmonic mean
pmean -- Power mean
kurtosis -- Fisher or Pearson kurtosis
mode -- Modal value
moment -- Central moment
lmoment
expectile -- Expectile
skew -- Skewness
kstat --
kstatvar --
tmean -- Truncated arithmetic mean
tvar -- Truncated variance
tmin --
tmax --
tstd --
tsem --
variation -- Coefficient of variation
find_repeats
rankdata
tiecorrect
trim_mean
gstd -- Geometric Standard Deviation
iqr
sem
bayes_mvs
mvsdist
entropy
differential_entropy
median_abs_deviation
Frequency statistics
====================
.. autosummary::
:toctree: generated/
cumfreq
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.
.. _hypotests:
Hypothesis Tests and related functions
======================================
SciPy has many functions for performing hypothesis tests that return a
test statistic and a p-value, and several of them return confidence intervals
and/or other related information.
The headings below are based on common uses of the functions within, but due to
the wide variety of statistical procedures, any attempt at coarse-grained
categorization will be imperfect. Also, note that tests within the same heading
are not interchangeable in general (e.g. many have different distributional
assumptions).
One Sample Tests / Paired Sample Tests
--------------------------------------
One sample tests are typically used to assess whether a single sample was
drawn from a specified distribution or a distribution with specified properties
(e.g. zero mean).
.. autosummary::
:toctree: generated/
ttest_1samp
binomtest
quantile_test
skewtest
kurtosistest
normaltest
jarque_bera
shapiro
anderson
cramervonmises
ks_1samp
goodness_of_fit
chisquare
power_divergence
Paired sample tests are often used to assess whether two samples were drawn
from the same distribution; they differ from the independent sample tests below
in that each observation in one sample is treated as paired with a
closely-related observation in the other sample (e.g. when environmental
factors are controlled between observations within a pair but not among pairs).
They can also be interpreted or used as one-sample tests (e.g. tests on the
mean or median of *differences* between paired observations).
.. autosummary::
:toctree: generated/
ttest_rel
wilcoxon
Association/Correlation Tests
-----------------------------
These tests are often used to assess whether there is a relationship (e.g.
linear) between paired observations in multiple samples or among the
coordinates of multivariate observations.
.. autosummary::
:toctree: generated/
linregress
pearsonr
spearmanr
pointbiserialr
kendalltau
chatterjeexi
weightedtau
somersd
siegelslopes
theilslopes
page_trend_test
multiscale_graphcorr
These association tests and are to work with samples in the form of contingency
tables. Supporting functions are available in `scipy.stats.contingency`.
.. autosummary::
:toctree: generated/
chi2_contingency
fisher_exact
barnard_exact
boschloo_exact
Independent Sample Tests
------------------------
Independent sample tests are typically used to assess whether multiple samples
were independently drawn from the same distribution or different distributions
with a shared property (e.g. equal means).
Some tests are specifically for comparing two samples.
.. autosummary::
:toctree: generated/
ttest_ind_from_stats
poisson_means_test
ttest_ind
mannwhitneyu
bws_test
ranksums
brunnermunzel
mood
ansari
cramervonmises_2samp
epps_singleton_2samp
ks_2samp
kstest
Others are generalized to multiple samples.
.. autosummary::
:toctree: generated/
f_oneway
tukey_hsd
dunnett
kruskal
alexandergovern
fligner
levene
bartlett
median_test
friedmanchisquare
anderson_ksamp
Resampling and Monte Carlo Methods
----------------------------------
The following functions can reproduce the p-value and confidence interval
results of most of the functions above, and often produce accurate results in a
wider variety of conditions. They can also be used to perform hypothesis tests
and generate confidence intervals for custom statistics. This flexibility comes
at the cost of greater computational requirements and stochastic results.
.. autosummary::
:toctree: generated/
monte_carlo_test
permutation_test
bootstrap
power
Instances of the following object can be passed into some hypothesis test
functions to perform a resampling or Monte Carlo version of the hypothesis
test.
.. autosummary::
:toctree: generated/
MonteCarloMethod
PermutationMethod
BootstrapMethod
Multiple Hypothesis Testing and Meta-Analysis
---------------------------------------------
These functions are for assessing the results of individual tests as a whole.
Functions for performing specific multiple hypothesis tests (e.g. post hoc
tests) are listed above.
.. autosummary::
:toctree: generated/
combine_pvalues
false_discovery_control
The following functions are related to the tests above but do not belong in the
above categories.
Random Variables
================
.. autosummary::
:toctree: generated/
make_distribution
Normal
Uniform
Mixture
order_statistic
truncate
abs
exp
log
Quasi-Monte Carlo
=================
.. toctree::
:maxdepth: 4
stats.qmc
Contingency Tables
==================
.. toctree::
:maxdepth: 4
stats.contingency
Masked statistics functions
===========================
.. toctree::
stats.mstats
Other statistical functionality
===============================
Transformations
---------------
.. autosummary::
:toctree: generated/
boxcox
boxcox_normmax
boxcox_llf
yeojohnson
yeojohnson_normmax
yeojohnson_llf
obrientransform
sigmaclip
trimboth
trim1
zmap
zscore
gzscore
Statistical distances
---------------------
.. autosummary::
:toctree: generated/
wasserstein_distance
wasserstein_distance_nd
energy_distance
Sampling
--------
.. toctree::
:maxdepth: 4
stats.sampling
Fitting / Survival Analysis
---------------------------
.. autosummary::
:toctree: generated/
fit
ecdf
logrank
Directional statistical functions
---------------------------------
.. autosummary::
:toctree: generated/
directional_stats
circmean
circvar
circstd
Sensitivity Analysis
--------------------
.. autosummary::
:toctree: generated/
sobol_indices
Plot-tests
----------
.. autosummary::
:toctree: generated/
ppcc_max
ppcc_plot
probplot
boxcox_normplot
yeojohnson_normplot
Univariate and multivariate kernel density estimation
-----------------------------------------------------
.. autosummary::
:toctree: generated/
gaussian_kde
Warnings / Errors used in :mod:`scipy.stats`
--------------------------------------------
.. autosummary::
:toctree: generated/
DegenerateDataWarning
ConstantInputWarning
NearConstantInputWarning
FitError
Result classes used in :mod:`scipy.stats`
-----------------------------------------
.. warning::
These classes are private, but they are included here because instances
of them are returned by other statistical functions. User import and
instantiation is not supported.
.. toctree::
:maxdepth: 2
stats._result_classes
""" # noqa: E501
from ._warnings_errors import (ConstantInputWarning, NearConstantInputWarning,
DegenerateDataWarning, FitError)
from ._stats_py import *
from ._variation import variation
from .distributions import *
from ._morestats import *
from ._multicomp import *
from ._binomtest import binomtest
from ._binned_statistic import *
from ._kde import gaussian_kde
from . import mstats
from . import qmc
from ._multivariate import *
from . import contingency
from .contingency import chi2_contingency
from ._censored_data import CensoredData
from ._resampling import (bootstrap, monte_carlo_test, permutation_test, power,
MonteCarloMethod, PermutationMethod, BootstrapMethod)
from ._entropy import *
from ._hypotests import *
from ._page_trend_test import page_trend_test
from ._mannwhitneyu import mannwhitneyu
from ._bws_test import bws_test
from ._fit import fit, goodness_of_fit
from ._covariance import Covariance
from ._sensitivity_analysis import *
from ._survival import *
from ._distribution_infrastructure import (
make_distribution, Mixture, order_statistic, truncate, exp, log, abs
)
from ._new_distributions import Normal, Uniform
from ._mgc import multiscale_graphcorr
from ._correlation import chatterjeexi
# Deprecated namespaces, to be removed in v2.0.0
from . import (
biasedurn, kde, morestats, mstats_basic, mstats_extras, mvn, stats
)
__all__ = [s for s in dir() if not s.startswith("_")] # Remove dunders.
from scipy._lib._testutils import PytestTester
test = PytestTester(__name__)
del PytestTester
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