Table of Contents
- Statistical functions (
scipy.stats)- Continuous distributions
- Multivariate distributions
- Discrete distributions
- Summary statistics
- Frequency statistics
- Correlation functions
- Statistical tests
- Transformations
- Statistical distances
- Random variate generation
- Circular statistical functions
- Contingency table functions
- Plot-tests
- Masked statistics functions
- Univariate and multivariate kernel density estimation (
scipy.stats.kde)
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Statistical functions (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):
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. |
frechet_r() |
A frechet_r continuous random variable. |
frechet_l() |
A frechet_l 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. |
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() |
General Kolmogorov-Smirnov one-sided test. |
kstwobign() |
Kolmogorov-Smirnov two-sided test for large N. |
laplace() |
A 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. |
lomax() |
A Lomax (Pareto of the second kind) continuous random variable. |
maxwell() |
A Maxwell continuous random variable. |
mielke() |
A Mielke’s Beta-Kappa 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 continuous random variable. |
reciprocal() |
A reciprocal 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. |
skewnorm() |
A skew-normal random variable. |
t() |
A Student’s t continuous random variable. |
trapz() |
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. |
Discrete distributions¶
bernoulli() |
A Bernoulli 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. |
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. |
zipf() |
A Zipf discrete random variable. |
yulesimon() |
A Yule-Simon discrete random variable. |
An overview of statistical functions is given below.
Several 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]) |
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 skewness of a data set. |
kstat(data[, n]) |
Return the nth k-statistic (1<=n<=4 so far). |
kstatvar(data[, n]) |
Returns 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]) |
Compute the coefficient of variation, the ratio of the biased standard deviation to the mean. |
find_repeats(arr) |
Find repeats and repeat counts. |
trim_mean(a, proportiontocut[, axis]) |
Return mean of array after trimming distribution from both tails. |
iqr(x[, axis, rng, scale, nan_policy, …]) |
Compute the interquartile range of the data along the specified axis. |
sem(a[, axis, ddof, nan_policy]) |
Calculate the standard error of the mean (or standard error of measurement) of the values in the input array. |
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]) |
Calculate the entropy of a distribution for given probability values. |
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]) |
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) |
Performs a 1-way ANOVA. |
pearsonr(x, y) |
Calculate a Pearson correlation coefficient and the p-value for testing non-correlation. |
spearmanr(a[, b, axis, nan_policy]) |
Calculate a Spearman rank-order correlation coefficient and the p-value to test for non-correlation. |
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 \(\tau\). |
linregress(x[, y]) |
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). |
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, nan_policy]) |
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]) |
Calculate the T-test on TWO RELATED samples of scores, a and b. |
kstest(rvs, cdf[, args, N, alternative, mode]) |
Perform the Kolmogorov-Smirnov test for goodness of fit. |
chisquare(f_obs[, f_exp, ddof, axis]) |
Calculate a one-way chi square test. |
power_divergence(f_obs[, f_exp, ddof, axis, …]) |
Cressie-Read power divergence statistic and goodness of fit test. |
ks_2samp(data1, data2) |
Compute the Kolmogorov-Smirnov statistic on 2 samples. |
mannwhitneyu(x, y[, use_continuity, alternative]) |
Compute the Mann-Whitney rank test on samples x and y. |
tiecorrect(rankvals) |
Tie correction factor for ties in the Mann-Whitney U and Kruskal-Wallis H tests. |
rankdata(a[, method]) |
Assign ranks to data, dealing with ties appropriately. |
ranksums(x, y) |
Compute the Wilcoxon rank-sum statistic for two samples. |
wilcoxon(x[, y, zero_method, correction]) |
Calculate the Wilcoxon signed-rank test. |
kruskal(\*args, \*\*kwargs) |
Compute the Kruskal-Wallis H-test for independent samples |
friedmanchisquare(\*args) |
Compute the Friedman test for repeated measurements |
brunnermunzel(x, y[, alternative, …]) |
Computes the Brunner-Munzel test on samples x and y |
combine_pvalues(pvalues[, method, weights]) |
Methods for combining the p-values of independent tests bearing upon the same hypothesis. |
jarque_bera(x) |
Perform the Jarque-Bera goodness of fit test on sample data. |
ansari(x, y) |
Perform the Ansari-Bradley test for equal scale parameters |
bartlett(\*args) |
Perform Bartlett’s test for equal variances |
levene(\*args, \*\*kwds) |
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. |
fligner(\*args, \*\*kwds) |
Perform Fligner-Killeen test for equality of variance. |
median_test(\*args, \*\*kwds) |
Mood’s median test. |
mood(x, y[, axis]) |
Perform Mood’s test for equal scale parameters. |
skewtest(a[, axis, nan_policy]) |
Test whether the skew is different from the normal distribution. |
kurtosistest(a[, axis, nan_policy]) |
Test whether a dataset has normal kurtosis. |
normaltest(a[, axis, nan_policy]) |
Test whether a sample differs from a normal distribution. |
Transformations¶
boxcox(x[, lmbda, alpha]) |
Return a positive dataset transformed by a Box-Cox power transformation. |
boxcox_normmax(x[, brack, method]) |
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 for input data, using maximum likelihood estimation. |
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]) |
Iterative sigma-clipping of array elements. |
trimboth(a, proportiontocut[, axis]) |
Slices off a proportion of items from both ends of an array. |
trim1(a, proportiontocut[, tail, axis]) |
Slices off a proportion from ONE end of the passed array distribution. |
zmap(scores, compare[, axis, ddof]) |
Calculate the relative z-scores. |
zscore(a[, axis, ddof]) |
Calculate the z score of each value in the sample, relative to the sample mean and standard deviation. |
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¶
rvs_ratio_uniforms(pdf, umax, vmin, vmax[, …]) |
Generate random samples from a probability density function using the ratio-of-uniforms method. |
Circular statistical functions¶
circmean(samples[, high, low, axis]) |
Compute the circular mean for samples in a range. |
circvar(samples[, high, low, axis]) |
Compute the circular variance for samples assumed to be in a range |
circstd(samples[, high, low, axis]) |
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.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. |
fisher_exact(table[, alternative]) |
Performs a Fisher 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. |
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
- 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.ks_2samp
- 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
- Other
- Summary statistics
Univariate and multivariate kernel density estimation (scipy.stats.kde)¶
gaussian_kde(dataset[, bw_method, weights]) |
Representation of a kernel-density estimate using Gaussian kernels. |
For many more stat related functions install the software R and the interface package rpy.