""" .. _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 `__: regression, linear models, time series analysis, extensions to topics also covered by ``scipy.stats``. - `Pandas `__: tabular data, time series functionality, interfaces to other statistical languages. - `PyMC3 `__: Bayesian statistical modeling, probabilistic machine learning. - `scikit-learn `__: classification, regression, model selection. - `Seaborn `__: statistical data visualization. - `rpy2 `__: 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 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 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 -- 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. 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 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 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 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 Discrete distributions ---------------------- .. autosummary:: :toctree: generated/ bernoulli -- Bernoulli betabinom -- Beta-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 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 kurtosis -- Fisher or Pearson kurtosis mode -- Modal value moment -- Central moment skew -- Skewness kstat -- kstatvar -- tmean -- Truncated arithmetic mean tvar -- Truncated variance tmin -- tmax -- tstd -- tsem -- variation -- Coefficient of variation find_repeats trim_mean gstd -- Geometric Standard Deviation iqr sem bayes_mvs mvsdist entropy differential_entropy median_absolute_deviation median_abs_deviation bootstrap Frequency statistics ==================== .. autosummary:: :toctree: generated/ cumfreq 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. Correlation functions ===================== .. autosummary:: :toctree: generated/ f_oneway alexandergovern pearsonr spearmanr pointbiserialr kendalltau weightedtau somersd linregress siegelslopes theilslopes multiscale_graphcorr Statistical tests ================= .. autosummary:: :toctree: generated/ ttest_1samp ttest_ind ttest_ind_from_stats ttest_rel chisquare cramervonmises cramervonmises_2samp power_divergence kstest ks_1samp ks_2samp epps_singleton_2samp mannwhitneyu tiecorrect rankdata ranksums wilcoxon kruskal friedmanchisquare brunnermunzel combine_pvalues jarque_bera page_trend_test .. autosummary:: :toctree: generated/ ansari bartlett levene shapiro anderson anderson_ksamp binom_test binomtest fligner median_test mood skewtest kurtosistest normaltest Quasi-Monte Carlo ================= .. toctree:: :maxdepth: 4 stats.qmc 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 Statistical distances --------------------- .. autosummary:: :toctree: generated/ wasserstein_distance energy_distance Random variate generation / CDF Inversion ========================================= .. autosummary:: :toctree: generated/ rvs_ratio_uniforms NumericalInverseHermite Circular statistical functions ------------------------------ .. autosummary:: :toctree: generated/ circmean circvar circstd Contingency table functions --------------------------- .. autosummary:: :toctree: generated/ chi2_contingency contingency.crosstab contingency.expected_freq contingency.margins contingency.relative_risk contingency.association fisher_exact barnard_exact boschloo_exact 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 used in :mod:`scipy.stats` ----------------------------------- .. autosummary:: :toctree: generated/ F_onewayConstantInputWarning F_onewayBadInputSizesWarning PearsonRConstantInputWarning PearsonRNearConstantInputWarning SpearmanRConstantInputWarning """ from .stats import * from .distributions import * from .morestats 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 ._bootstrap import bootstrap from ._entropy import * from ._hypotests import * from ._rvs_sampling import rvs_ratio_uniforms, NumericalInverseHermite from ._page_trend_test import page_trend_test from ._mannwhitneyu import mannwhitneyu __all__ = [s for s in dir() if not s.startswith("_")] # Remove dunders. from scipy._lib._testutils import PytestTester test = PytestTester(__name__) del PytestTester