# Statistical functions (`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):

`rv_continuous`([momtype, a, b, xtol, …]) | A generic continuous random variable class meant for subclassing.
`rv_discrete`([a, b, name, badvalue, …]) | A generic discrete random variable class meant for subclassing.
`rv_histogram`(histogram, *args, **kwargs) | Generates a distribution given by a histogram.

### Continuous distributions

`alpha` | An alpha continuous random variable.
`anglit` | An anglit continuous random variable.
`arcsine` | An arcsine continuous random variable.
`argus` | Argus distribution
`beta` | A beta continuous random variable.
`betaprime` | A beta prime continuous random variable.
`bradford` | A Bradford continuous random variable.
`burr` | A Burr (Type III) continuous random variable.
`burr12` | A Burr (Type XII) continuous random variable.
`cauchy` | A Cauchy continuous random variable.
`chi` | A chi continuous random variable.
`chi2` | A chi-squared continuous random variable.
`cosine` | A cosine continuous random variable.
`crystalball` | Crystalball distribution
`dgamma` | A double gamma continuous random variable.
`dweibull` | A double Weibull continuous random variable.
`erlang` | An Erlang continuous random variable.
`expon` | An exponential continuous random variable.
`exponnorm` | An exponentially modified Normal continuous random variable.
`exponweib` | An exponentiated Weibull continuous random variable.
`exponpow` | An exponential power continuous random variable.
`f` | An F continuous random variable.
`fatiguelife` | A fatigue-life (Birnbaum-Saunders) continuous random variable.
`fisk` | A Fisk continuous random variable.
`foldcauchy` | A folded Cauchy continuous random variable.
`foldnorm` | A folded normal continuous random variable.
`genlogistic` | A generalized logistic continuous random variable.
`gennorm` | A generalized normal continuous random variable.
`genpareto` | A generalized Pareto continuous random variable.
`genexpon` | A generalized exponential continuous random variable.
`genextreme` | A generalized extreme value continuous random variable.
`gausshyper` | A Gauss hypergeometric continuous random variable.
`gamma` | A gamma continuous random variable.
`gengamma` | A generalized gamma continuous random variable.
`genhalflogistic` | A generalized half-logistic continuous random variable.
`genhyperbolic` | A generalized hyperbolic continuous random variable.
`geninvgauss` | A Generalized Inverse Gaussian continuous random variable.
`gilbrat` | A Gilbrat continuous random variable.
`gompertz` | A Gompertz (or truncated Gumbel) continuous random variable.
`gumbel_r` | A right-skewed Gumbel continuous random variable.
`gumbel_l` | A left-skewed Gumbel continuous random variable.
`halfcauchy` | A Half-Cauchy continuous random variable.
`halflogistic` | A half-logistic continuous random variable.
`halfnorm` | A half-normal continuous random variable.
`halfgennorm` | The upper half of a generalized normal continuous random variable.
`hypsecant` | A hyperbolic secant continuous random variable.
`invgamma` | An inverted gamma continuous random variable.
`invgauss` | An inverse Gaussian continuous random variable.
`invweibull` | An inverted Weibull continuous random variable.
`johnsonsb` | A Johnson SB continuous random variable.
`johnsonsu` | A Johnson SU continuous random variable.
`kappa4` | Kappa 4 parameter distribution.
`kappa3` | Kappa 3 parameter distribution.
`ksone` | Kolmogorov-Smirnov one-sided test statistic distribution.
`kstwo` | Kolmogorov-Smirnov two-sided test statistic distribution.
`kstwobign` | Limiting distribution of scaled Kolmogorov-Smirnov two-sided test statistic.
`laplace` | A Laplace continuous random variable.
`laplace_asymmetric` | An asymmetric Laplace continuous random variable.
`levy` | A Levy continuous random variable.
`levy_l` | A left-skewed Levy continuous random variable.
`levy_stable` | A Levy-stable continuous random variable.
`logistic` | A logistic (or Sech-squared) continuous random variable.
`loggamma` | A log gamma continuous random variable.
`loglaplace` | A log-Laplace continuous random variable.
`lognorm` | A lognormal continuous random variable.
`loguniform` | A loguniform or reciprocal continuous random variable.
`lomax` | A Lomax (Pareto of the second kind) continuous random variable.
`maxwell` | A Maxwell continuous random variable.
`mielke` | A Mielke Beta-Kappa / Dagum continuous random variable.
`moyal` | A Moyal continuous random variable.
`nakagami` | A Nakagami continuous random variable.
`ncx2` | A non-central chi-squared continuous random variable.
`ncf` | A non-central F distribution continuous random variable.
`nct` | A non-central Student’s t continuous random variable.
`norm` | A normal continuous random variable.
`norminvgauss` | A Normal Inverse Gaussian continuous random variable.
`pareto` | A Pareto continuous random variable.
`pearson3` | A pearson type III continuous random variable.
`powerlaw` | A power-function continuous random variable.
`powerlognorm` | A power log-normal continuous random variable.
`powernorm` | A power normal continuous random variable.
`rdist` | An R-distributed (symmetric beta) continuous random variable.
`rayleigh` | A Rayleigh continuous random variable.
`rice` | A Rice continuous random variable.
`recipinvgauss` | A reciprocal inverse Gaussian continuous random variable.
`semicircular` | A semicircular continuous random variable.
`skewcauchy` | A skewed Cauchy random variable.
`skewnorm` | A skew-normal random variable.
`studentized_range` | A studentized range continuous random variable.
`t` | A Student’s t continuous random variable.
`trapezoid` | A trapezoidal continuous random variable.
`triang` | A triangular continuous random variable.
`truncexpon` | A truncated exponential continuous random variable.
`truncnorm` | A truncated normal continuous random variable.
`tukeylambda` | A Tukey-Lamdba continuous random variable.
`uniform` | A uniform continuous random variable.
`vonmises` | A Von Mises continuous random variable.
`vonmises_line` | A Von Mises continuous random variable.
`wald` | A Wald continuous random variable.
`weibull_min` | Weibull minimum continuous random variable.
`weibull_max` | Weibull maximum continuous random variable.
`wrapcauchy` | A wrapped Cauchy continuous random variable.

### Multivariate distributions

`multivariate_normal` | A multivariate normal random variable.
`matrix_normal` | A matrix normal random variable.
`dirichlet` | A Dirichlet random variable.
`wishart` | A Wishart random variable.
`invwishart` | An inverse Wishart random variable.
`multinomial` | A multinomial random variable.
`special_ortho_group` | A matrix-valued SO(N) random variable.
`ortho_group` | A matrix-valued O(N) random variable.
`unitary_group` | A matrix-valued U(N) random variable.
`random_correlation` | A random correlation matrix.
`multivariate_t` | A multivariate t-distributed random variable.
`multivariate_hypergeom` | A multivariate hypergeometric random variable.

### Discrete distributions

`bernoulli` | A Bernoulli discrete random variable.
`betabinom` | A beta-binomial discrete random variable.
`binom` | A binomial discrete random variable.
`boltzmann` | A Boltzmann (Truncated Discrete Exponential) random variable.
`dlaplace` | A Laplacian discrete random variable.
`geom` | A geometric discrete random variable.
`hypergeom` | A hypergeometric discrete random variable.
`logser` | A Logarithmic (Log-Series, Series) discrete random variable.
`nbinom` | A negative binomial discrete random variable.
`nchypergeom_fisher` | A Fisher’s noncentral hypergeometric discrete random variable.
`nchypergeom_wallenius` | A Wallenius’ noncentral hypergeometric discrete random variable.
`nhypergeom` | A negative hypergeometric discrete random variable.
`planck` | A Planck discrete exponential random variable.
`poisson` | A Poisson discrete random variable.
`randint` | A uniform discrete random variable.
`skellam` | A Skellam discrete random variable.
`yulesimon` | A Yule-Simon discrete random variable.
`zipf` | A Zipf (Zeta) discrete random variable.
`zipfian` | A Zipfian discrete random variable.

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

`describe`(a[, axis, ddof, bias, nan_policy]) | Compute several descriptive statistics of the passed array.
`gmean`(a[, axis, dtype, weights]) | Compute the geometric mean along the specified axis.
`hmean`(a[, axis, dtype]) | Calculate the harmonic mean along the specified axis.
`kurtosis`(a[, axis, fisher, bias, nan_policy]) | Compute the kurtosis (Fisher or Pearson) of a dataset.
`mode`(a[, axis, nan_policy]) | Return an array of the modal (most common) value in the passed array.
`moment`(a[, moment, axis, nan_policy]) | Calculate the nth moment about the mean for a sample.
`skew`(a[, axis, bias, nan_policy]) | Compute the sample skewness of a data set.
`kstat`(data[, n]) | Return the nth k-statistic (1<=n<=4 so far).
`kstatvar`(data[, n]) | Return an unbiased estimator of the variance of the k-statistic.
`tmean`(a[, limits, inclusive, axis]) | Compute the trimmed mean.
`tvar`(a[, limits, inclusive, axis, ddof]) | Compute the trimmed variance.
`tmin`(a[, lowerlimit, axis, inclusive, …]) | Compute the trimmed minimum.
`tmax`(a[, upperlimit, axis, inclusive, …]) | Compute the trimmed maximum.
`tstd`(a[, limits, inclusive, axis, ddof]) | Compute the trimmed sample standard deviation.
`tsem`(a[, limits, inclusive, axis, ddof]) | Compute the trimmed standard error of the mean.
`variation`(a[, axis, nan_policy, ddof]) | Compute the coefficient of variation.
`find_repeats`(arr) | Find repeats and repeat counts.
`trim_mean`(a, proportiontocut[, axis]) | Return mean of array after trimming distribution from both tails.
`gstd`(a[, axis, ddof]) | Calculate the geometric standard deviation of an array.
`iqr`(x[, axis, rng, scale, nan_policy, …]) | Compute the interquartile range of the data along the specified axis.
`sem`(a[, axis, ddof, nan_policy]) | Compute standard error of the mean.
`bayes_mvs`(data[, alpha]) | Bayesian confidence intervals for the mean, var, and std.
`mvsdist`(data) | ‘Frozen’ distributions for mean, variance, and standard deviation of data.
`entropy`(pk[, qk, base, axis]) | Calculate the entropy of a distribution for given probability values.
`differential_entropy`(values, *[, …]) | Given a sample of a distribution, estimate the differential entropy.
`median_absolute_deviation`(*args, **kwds) | `median_absolute_deviation` is deprecated, use `median_abs_deviation` instead!
`median_abs_deviation`(x[, axis, center, …]) | Compute the median absolute deviation of the data along the given axis.
`bootstrap`(data, statistic, *[, vectorized, …]) | Compute a two-sided bootstrap confidence interval of a statistic.

## Frequency statistics

`cumfreq`(a[, numbins, defaultreallimits, weights]) | Return a cumulative frequency histogram, using the histogram function.
`itemfreq`(*args, **kwds) | `itemfreq` is deprecated! `itemfreq` is deprecated and will be removed in a future version.
`percentileofscore`(a, score[, kind]) | Compute the percentile rank of a score relative to a list of scores.
`scoreatpercentile`(a, per[, limit, …]) | Calculate the score at a given percentile of the input sequence.
`relfreq`(a[, numbins, defaultreallimits, weights]) | Return a relative frequency histogram, using the histogram function.

`binned_statistic`(x, values[, statistic, …]) | Compute a binned statistic for one or more sets of data.
`binned_statistic_2d`(x, y, values[, …]) | Compute a bidimensional binned statistic for one or more sets of data.
`binned_statistic_dd`(sample, values[, …]) | Compute a multidimensional binned statistic for a set of data.

## Correlation functions

`f_oneway`(*args[, axis]) | Perform one-way ANOVA.
`alexandergovern`(*args[, nan_policy]) | Performs the Alexander Govern test.
`pearsonr`(x, y) | Pearson correlation coefficient and p-value for testing non-correlation.
`spearmanr`(a[, b, axis, nan_policy, alternative]) | Calculate a Spearman correlation coefficient with associated p-value.
`pointbiserialr`(x, y) | Calculate a point biserial correlation coefficient and its p-value.
`kendalltau`(x, y[, initial_lexsort, …]) | Calculate Kendall’s tau, a correlation measure for ordinal data.
`weightedtau`(x, y[, rank, weigher, additive]) | Compute a weighted version of Kendall’s \(\tau\).
`somersd`(x[, y]) | Calculates Somers’ D, an asymmetric measure of ordinal association.
`linregress`(x[, y, alternative]) | Calculate a linear least-squares regression for two sets of measurements.
`siegelslopes`(y[, x, method]) | Computes the Siegel estimator for a set of points (x, y).
`theilslopes`(y[, x, alpha]) | Computes the Theil-Sen estimator for a set of points (x, y).
`multiscale_graphcorr`(x, y[, …]) | Computes the Multiscale Graph Correlation (MGC) test statistic.

## Statistical tests

`ttest_1samp`(a, popmean[, axis, nan_policy, …]) | Calculate the T-test for the mean of ONE group of scores.
`ttest_ind`(a, b[, axis, equal_var, …]) | Calculate the T-test for the means of two independent samples of scores.
`ttest_ind_from_stats`(mean1, std1, nobs1, …) | T-test for means of two independent samples from descriptive statistics.
`ttest_rel`(a, b[, axis, nan_policy, alternative]) | Calculate the t-test on TWO RELATED samples of scores, a and b.
`chisquare`(f_obs[, f_exp, ddof, axis]) | Calculate a one-way chi-square test.
`cramervonmises`(rvs, cdf[, args]) | Perform the one-sample Cramér-von Mises test for goodness of fit.
`cramervonmises_2samp`(x, y[, method]) | Perform the two-sample Cramér-von Mises test for goodness of fit.
`power_divergence`(f_obs[, f_exp, ddof, axis, …]) | Cressie-Read power divergence statistic and goodness of fit test.
`kstest`(rvs, cdf[, args, N, alternative, mode]) | Performs the (one-sample or two-sample) Kolmogorov-Smirnov test for goodness of fit.
`ks_1samp`(x, cdf[, args, alternative, mode]) | Performs the one-sample Kolmogorov-Smirnov test for goodness of fit.
`ks_2samp`(data1, data2[, alternative, mode]) | Performs the two-sample Kolmogorov-Smirnov test for goodness of fit.
`epps_singleton_2samp`(x, y[, t]) | Compute the Epps-Singleton (ES) test statistic.
`mannwhitneyu`(x, y[, use_continuity, …]) | Perform the Mann-Whitney U rank test on two independent samples.
`tiecorrect`(rankvals) | Tie correction factor for Mann-Whitney U and Kruskal-Wallis H tests.
`rankdata`(a[, method, axis]) | Assign ranks to data, dealing with ties appropriately.
`ranksums`(x, y[, alternative]) | Compute the Wilcoxon rank-sum statistic for two samples.
`wilcoxon`(x[, y, zero_method, correction, …]) | Calculate the Wilcoxon signed-rank test.
`kruskal`(*args[, nan_policy]) | Compute the Kruskal-Wallis H-test for independent samples.
`friedmanchisquare`(*args) | Compute the Friedman test for repeated measurements.
`brunnermunzel`(x, y[, alternative, …]) | Compute the Brunner-Munzel test on samples x and y.
`combine_pvalues`(pvalues[, method, weights]) | Combine p-values from independent tests bearing upon the same hypothesis.
`jarque_bera`(x) | Perform the Jarque-Bera goodness of fit test on sample data.
`page_trend_test`(data[, ranked, …]) | Perform Page’s Test, a measure of trend in observations between treatments.

`ansari`(x, y[, alternative]) | Perform the Ansari-Bradley test for equal scale parameters.
`bartlett`(*args) | Perform Bartlett’s test for equal variances.
`levene`(*args[, center, proportiontocut]) | Perform Levene test for equal variances.
`shapiro`(x) | Perform the Shapiro-Wilk test for normality.
`anderson`(x[, dist]) | Anderson-Darling test for data coming from a particular distribution.
`anderson_ksamp`(samples[, midrank]) | The Anderson-Darling test for k-samples.
`binom_test`(x[, n, p, alternative]) | Perform a test that the probability of success is p.
`binomtest`(k, n[, p, alternative]) | Perform a test that the probability of success is p.
`fligner`(*args[, center, proportiontocut]) | Perform Fligner-Killeen test for equality of variance.
`median_test`(*args[, ties, correction, …]) | Perform a Mood’s median test.
`mood`(x, y[, axis, alternative]) | Perform Mood’s test for equal scale parameters.
`skewtest`(a[, axis, nan_policy, alternative]) | Test whether the skew is different from the normal distribution.
`kurtosistest`(a[, axis, nan_policy, alternative]) | Test whether a dataset has normal kurtosis.
`normaltest`(a[, axis, nan_policy]) | Test whether a sample differs from a normal distribution.

## Quasi-Monte Carlo

- Quasi-Monte Carlo submodule (`scipy.stats.qmc`)
  - Quasi-Monte Carlo
    - Engines
      - scipy.stats.qmc.QMCEngine
      - scipy.stats.qmc.Sobol
      - scipy.stats.qmc.Halton
      - scipy.stats.qmc.LatinHypercube
      - scipy.stats.qmc.MultinomialQMC
      - scipy.stats.qmc.MultivariateNormalQMC
    - Helpers
      - scipy.stats.qmc.discrepancy
      - scipy.stats.qmc.update_discrepancy
      - scipy.stats.qmc.scale
  - Introduction to Quasi-Monte Carlo
    - References

## Masked statistics functions

- Statistical functions for masked arrays (`scipy.stats.mstats`)
  - Summary statistics
    - scipy.stats.mstats.describe
    - scipy.stats.mstats.gmean
    - scipy.stats.mstats.hmean
    - scipy.stats.mstats.kurtosis
    - scipy.stats.mstats.mode
    - scipy.stats.mstats.mquantiles
    - scipy.stats.mstats.hdmedian
    - scipy.stats.mstats.hdquantiles
    - scipy.stats.mstats.hdquantiles_sd
    - scipy.stats.mstats.idealfourths
    - scipy.stats.mstats.plotting_positions
    - scipy.stats.mstats.meppf
    - scipy.stats.mstats.moment
    - scipy.stats.mstats.skew
    - scipy.stats.mstats.tmean
    - scipy.stats.mstats.tvar
    - scipy.stats.mstats.tmin
    - scipy.stats.mstats.tmax
    - scipy.stats.mstats.tsem
    - scipy.stats.mstats.variation
    - scipy.stats.mstats.find_repeats
    - scipy.stats.mstats.sem
    - scipy.stats.mstats.trimmed_mean
    - scipy.stats.mstats.trimmed_mean_ci
    - scipy.stats.mstats.trimmed_std
    - scipy.stats.mstats.trimmed_var
  - Frequency statistics
    - scipy.stats.mstats.scoreatpercentile
  - Correlation functions
    - scipy.stats.mstats.f_oneway
    - scipy.stats.mstats.pearsonr
    - scipy.stats.mstats.spearmanr
    - scipy.stats.mstats.pointbiserialr
    - scipy.stats.mstats.kendalltau
    - scipy.stats.mstats.kendalltau_seasonal
    - scipy.stats.mstats.linregress
    - scipy.stats.mstats.siegelslopes
    - scipy.stats.mstats.theilslopes
    - scipy.stats.mstats.sen_seasonal_slopes
  - Statistical tests
    - scipy.stats.mstats.ttest_1samp
    - scipy.stats.mstats.ttest_onesamp
    - scipy.stats.mstats.ttest_ind
    - scipy.stats.mstats.ttest_rel
    - scipy.stats.mstats.chisquare
    - scipy.stats.mstats.kstest
    - scipy.stats.mstats.ks_2samp
    - scipy.stats.mstats.ks_1samp
    - scipy.stats.mstats.ks_twosamp
    - scipy.stats.mstats.mannwhitneyu
    - scipy.stats.mstats.rankdata
    - scipy.stats.mstats.kruskal
    - scipy.stats.mstats.kruskalwallis
    - scipy.stats.mstats.friedmanchisquare
    - scipy.stats.mstats.brunnermunzel
    - scipy.stats.mstats.skewtest
    - scipy.stats.mstats.kurtosistest
    - scipy.stats.mstats.normaltest
  - Transformations
    - scipy.stats.mstats.obrientransform
    - scipy.stats.mstats.trim
    - scipy.stats.mstats.trima
    - scipy.stats.mstats.trimmed_stde
    - scipy.stats.mstats.trimr
    - scipy.stats.mstats.trimtail
    - scipy.stats.mstats.trimboth
    - scipy.stats.mstats.winsorize
    - scipy.stats.mstats.zmap
    - scipy.stats.mstats.zscore
  - Other
    - scipy.stats.mstats.argstoarray
    - scipy.stats.mstats.count_tied_groups
    - scipy.stats.mstats.msign
    - scipy.stats.mstats.compare_medians_ms
    - scipy.stats.mstats.median_cihs
    - scipy.stats.mstats.mjci
    - scipy.stats.mstats.mquantiles_cimj
    - scipy.stats.mstats.rsh

## Other statistical functionality

### Transformations

`boxcox`(x[, lmbda, alpha, optimizer]) | Return a dataset transformed by a Box-Cox power transformation.
`boxcox_normmax`(x[, brack, method, optimizer]) | Compute optimal Box-Cox transform parameter for input data.
`boxcox_llf`(lmb, data) | The boxcox log-likelihood function.
`yeojohnson`(x[, lmbda]) | Return a dataset transformed by a Yeo-Johnson power transformation.
`yeojohnson_normmax`(x[, brack]) | Compute optimal Yeo-Johnson transform parameter.
`yeojohnson_llf`(lmb, data) | The yeojohnson log-likelihood function.
`obrientransform`(*args) | Compute the O’Brien transform on input data (any number of arrays).
`sigmaclip`(a[, low, high]) | Perform iterative sigma-clipping of array elements.
`trimboth`(a, proportiontocut[, axis]) | Slice off a proportion of items from both ends of an array.
`trim1`(a, proportiontocut[, tail, axis]) | Slice off a proportion from ONE end of the passed array distribution.
`zmap`(scores, compare[, axis, ddof, nan_policy]) | Calculate the relative z-scores.
`zscore`(a[, axis, ddof, nan_policy]) | Compute the z score.

### Statistical distances

`wasserstein_distance`(u_values, v_values[, …]) | Compute the first Wasserstein distance between two 1D distributions.
`energy_distance`(u_values, v_values[, …]) | Compute the energy distance between two 1D distributions.

## Random variate generation / CDF Inversion

`rvs_ratio_uniforms`(pdf, umax, vmin, vmax[, …]) | Generate random samples from a probability density function using the ratio-of-uniforms method.
`NumericalInverseHermite`(dist, *[, tol, …]) | A Hermite spline fast numerical inverse of a probability distribution.

### Circular statistical functions

`circmean`(samples[, high, low, axis, nan_policy]) | Compute the circular mean for samples in a range.
`circvar`(samples[, high, low, axis, nan_policy]) | Compute the circular variance for samples assumed to be in a range.
`circstd`(samples[, high, low, axis, nan_policy]) | Compute the circular standard deviation for samples assumed to be in the range [low to high].

### Contingency table functions

`chi2_contingency`(observed[, correction, lambda_]) | Chi-square test of independence of variables in a contingency table.
`contingency.crosstab`(*args[, levels, sparse]) | Return table of counts for each possible unique combination in `*args`.
`contingency.expected_freq`(observed) | Compute the expected frequencies from a contingency table.
`contingency.margins`(a) | Return a list of the marginal sums of the array a.
`contingency.relative_risk`(exposed_cases, …) | Compute the relative risk (also known as the risk ratio).
`contingency.association`(observed[, method, …]) | Calculates degree of association between two nominal variables.
`fisher_exact`(table[, alternative]) | Perform a Fisher exact test on a 2x2 contingency table.
`barnard_exact`(table[, alternative, pooled, n]) | Perform a Barnard exact test on a 2x2 contingency table.
`boschloo_exact`(table[, alternative, n]) | Perform Boschloo’s exact test on a 2x2 contingency table.

### Plot-tests

`ppcc_max`(x[, brack, dist]) | Calculate the shape parameter that maximizes the PPCC.
`ppcc_plot`(x, a, b[, dist, plot, N]) | Calculate and optionally plot probability plot correlation coefficient.
`probplot`(x[, sparams, dist, fit, plot, rvalue]) | Calculate quantiles for a probability plot, and optionally show the plot.
`boxcox_normplot`(x, la, lb[, plot, N]) | Compute parameters for a Box-Cox normality plot, optionally show it.
`yeojohnson_normplot`(x, la, lb[, plot, N]) | Compute parameters for a Yeo-Johnson normality plot, optionally show it.

### Univariate and multivariate kernel density estimation

`gaussian_kde`(dataset[, bw_method, weights]) | Representation of a kernel-density estimate using Gaussian kernels.

### Warnings used in `scipy.stats`

`F_onewayConstantInputWarning`([msg]) | Warning generated by `f_oneway` when an input is constant, e.g.
`F_onewayBadInputSizesWarning` | Warning generated by `f_oneway` when an input has length 0, or if all the inputs have length 1.
`PearsonRConstantInputWarning`([msg]) | Warning generated by `pearsonr` when an input is constant.
`PearsonRNearConstantInputWarning`([msg]) | Warning generated by `pearsonr` when an input is nearly constant.
`SpearmanRConstantInputWarning`([msg]) | Warning generated by `spearmanr` when an input is constant.

scipy.special.sinc scipy.stats.rv_continuous