Statistical functions (scipy.stats)¶
This module contains a large number of probability distributions as well as a growing library of statistical functions.
Each included distribution is an instance of the class rv_continuous: For each given name the following methods are available:
| rv_continuous([momtype, a, b, xtol, ...]) | A generic continuous random variable class meant for subclassing. |
| rv_continuous.pdf(x, *args, **kwds) | Probability density function at x of the given RV. |
| rv_continuous.logpdf(x, *args, **kwds) | Log of the probability density function at x of the given RV. |
| rv_continuous.cdf(x, *args, **kwds) | Cumulative distribution function of the given RV. |
| rv_continuous.logcdf(x, *args, **kwds) | Log of the cumulative distribution function at x of the given RV. |
| rv_continuous.sf(x, *args, **kwds) | Survival function (1-cdf) at x of the given RV. |
| rv_continuous.logsf(x, *args, **kwds) | Log of the survival function of the given RV. |
| rv_continuous.ppf(q, *args, **kwds) | Percent point function (inverse of cdf) at q of the given RV. |
| rv_continuous.isf(q, *args, **kwds) | Inverse survival function at q of the given RV. |
| rv_continuous.moment(n, *args, **kwds) | n’th order non-central moment of distribution. |
| rv_continuous.stats(*args, **kwds) | Some statistics of the given RV |
| rv_continuous.entropy(*args, **kwds) | Differential entropy of the RV. |
| rv_continuous.fit(data, *args, **kwds) | Return MLEs for shape, location, and scale parameters from data. |
| rv_continuous.expect([func, args, loc, ...]) | Calculate expected value of a function with respect to the distribution. |
Calling the instance as a function returns a frozen pdf whose shape, location, and scale parameters are fixed.
Similarly, each discrete distribution is an instance of the class rv_discrete:
| rv_discrete([a, b, name, badvalue, ...]) | A generic discrete random variable class meant for subclassing. |
| rv_discrete.rvs(*args, **kwargs) | Random variates of given type. |
| rv_discrete.pmf(k, *args, **kwds) | Probability mass function at k of the given RV. |
| rv_discrete.logpmf(k, *args, **kwds) | Log of the probability mass function at k of the given RV. |
| rv_discrete.cdf(k, *args, **kwds) | Cumulative distribution function of the given RV. |
| rv_discrete.logcdf(k, *args, **kwds) | Log of the cumulative distribution function at k of the given RV |
| rv_discrete.sf(k, *args, **kwds) | Survival function (1-cdf) at k of the given RV. |
| rv_discrete.logsf(k, *args, **kwds) | Log of the survival function of the given RV. |
| rv_discrete.ppf(q, *args, **kwds) | Percent point function (inverse of cdf) at q of the given RV |
| rv_discrete.isf(q, *args, **kwds) | Inverse survival function (inverse of sf) at q of the given RV. |
| rv_discrete.stats(*args, **kwds) | Some statistics of the given RV |
| rv_discrete.moment(n, *args, **kwds) | n’th order non-central moment of distribution. |
| rv_discrete.entropy(*args, **kwds) | Differential entropy of the RV. |
| rv_discrete.expect([func, args, loc, lb, ...]) | Calculate expected value of a function with respect to the distribution |
Continuous distributions¶
| alpha | An alpha continuous random variable. |
| anglit | An anglit continuous random variable. |
| arcsine | An arcsine continuous random variable. |
| beta | A beta continuous random variable. |
| betaprime | A beta prime continuous random variable. |
| bradford | A Bradford continuous random variable. |
| burr | A Burr 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. |
| 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. |
| 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 right (or Weibull minimum) continuous random variable. |
| frechet_l | A Frechet left (or Weibull maximum) continuous random variable. |
| genlogistic | A generalized logistic 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. |
| 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. |
| ksone | General Kolmogorov-Smirnov one-sided test. |
| kstwobign | Kolmogorov-Smirnov two-sided test for large N. |
| laplace | A Laplace 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. |
| 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. |
| 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. |
| t | A Student’s T 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. |
| wald | A Wald continuous random variable. |
| weibull_min | A Frechet right (or Weibull minimum) continuous random variable. |
| weibull_max | A Frechet left (or Weibull maximum) continuous random variable. |
| wrapcauchy | A wrapped Cauchy continuous random variable. |
Multivariate distributions¶
| multivariate_normal | A multivariate normal random variable. |
| dirichlet | A Dirichlet random variable. |
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. |
Statistical functions¶
Several of these functions have a similar version in scipy.stats.mstats which work for masked arrays.
| describe(a[, axis, ddof]) | Computes several descriptive statistics of the passed array. |
| gmean(a[, axis, dtype]) | Compute the geometric mean along the specified axis. |
| hmean(a[, axis, dtype]) | Calculates the harmonic mean along the specified axis. |
| kurtosis(a[, axis, fisher, bias]) | Computes the kurtosis (Fisher or Pearson) of a dataset. |
| kurtosistest(a[, axis]) | Tests whether a dataset has normal kurtosis |
| mode(a[, axis]) | Returns an array of the modal (most common) value in the passed array. |
| moment(a[, moment, axis]) | Calculates the nth moment about the mean for a sample. |
| normaltest(a[, axis]) | Tests whether a sample differs from a normal distribution. |
| skew(a[, axis, bias]) | Computes the skewness of a data set. |
| skewtest(a[, axis]) | Tests whether the skew is different from the normal distribution. |
| tmean(a[, limits, inclusive]) | Compute the trimmed mean. |
| tvar(a[, limits, inclusive]) | 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]) | Compute the trimmed sample standard deviation |
| tsem(a[, limits, inclusive]) | Compute the trimmed standard error of the mean. |
| nanmean(*args, **kwds) | nanmean is deprecated! |
| nanstd(*args, **kwds) | nanstd is deprecated! |
| nanmedian(*args, **kwds) | nanmedian is deprecated! |
| variation(a[, axis]) | Computes the coefficient of variation, the ratio of the biased standard deviation to the mean. |
| cumfreq(a[, numbins, defaultreallimits, weights]) | Returns a cumulative frequency histogram, using the histogram function. |
| histogram2(a, bins) | Compute histogram using divisions in bins. |
| histogram(a[, numbins, defaultlimits, ...]) | Separates the range into several bins and returns the number of instances in each bin. |
| itemfreq(a) | Returns a 2-D array of item frequencies. |
| 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]) | Returns a relative frequency histogram, using the histogram function. |
| binned_statistic(x, values[, statistic, ...]) | Compute a binned statistic for a set of data. |
| binned_statistic_2d(x, y, values[, ...]) | Compute a bidimensional binned statistic for a set of data. |
| binned_statistic_dd(sample, values[, ...]) | Compute a multidimensional binned statistic for a set of data. |
| obrientransform(*args) | Computes the O’Brien transform on input data (any number of arrays). |
| signaltonoise(a[, axis, ddof]) | The signal-to-noise ratio of the input data. |
| bayes_mvs(data[, alpha]) | Bayesian confidence intervals for the mean, var, and std. |
| sem(a[, axis, ddof]) | Calculates the standard error of the mean (or standard error of measurement) of the values in the input array. |
| zmap(scores, compare[, axis, ddof]) | Calculates the relative z-scores. |
| zscore(a[, axis, ddof]) | Calculates the z score of each value in the sample, relative to the sample mean and standard deviation. |
| sigmaclip(a[, low, high]) | Iterative sigma-clipping of array elements. |
| threshold(a[, threshmin, threshmax, newval]) | Clip array to a given value. |
| trimboth(a, proportiontocut[, axis]) | Slices off a proportion of items from both ends of an array. |
| trim1(a, proportiontocut[, tail]) | Slices off a proportion of items from ONE end of the passed array distribution. |
| f_oneway(*args) | Performs a 1-way ANOVA. |
| pearsonr(x, y) | Calculates a Pearson correlation coefficient and the p-value for testing non-correlation. |
| spearmanr(a[, b, axis]) | Calculates a Spearman rank-order correlation coefficient and the p-value to test for non-correlation. |
| pointbiserialr(x, y) | Calculates a point biserial correlation coefficient and the associated p-value. |
| kendalltau(x, y[, initial_lexsort]) | Calculates Kendall’s tau, a correlation measure for ordinal data. |
| linregress(x[, y]) | Calculate a regression line |
| theilslopes(y[, x, alpha]) | Computes the Theil-Sen estimator for a set of points (x, y). |
| ttest_1samp(a, popmean[, axis]) | Calculates the T-test for the mean of ONE group of scores. |
| ttest_ind(a, b[, axis, equal_var]) | Calculates the T-test for the means of TWO INDEPENDENT samples of scores. |
| ttest_rel(a, b[, axis]) | Calculates 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]) | Calculates 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) | Computes the Kolmogorov-Smirnov statistic on 2 samples. |
| mannwhitneyu(x, y[, use_continuity]) | Computes 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) | Compute the Kruskal-Wallis H-test for independent samples |
| friedmanchisquare(*args) | Computes the Friedman test for repeated measurements |
| combine_pvalues(pvalues[, method, weights]) | Methods for combining the p-values of independent tests bearing upon the same hypothesis. |
| 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[, a, reta]) | 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]) | Perform a test that the probability of success is p. |
| fligner(*args, **kwds) | Perform Fligner’s test for equal variances. |
| median_test(*args, **kwds) | Mood’s median test. |
| mood(x, y[, axis]) | Perform Mood’s test for equal scale parameters. |
| 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. |
| entropy(pk[, qk, base]) | Calculate the entropy of a distribution for given probability values. |
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]) | Returns the shape parameter that maximizes the probability plot correlation coefficient for the given data to a one-parameter family of distributions. |
| ppcc_plot(x, a, b[, dist, plot, N]) | Returns (shape, ppcc), and optionally plots shape vs. |
| probplot(x[, sparams, dist, fit, plot]) | 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. |
Masked statistics functions¶
- Statistical functions for masked arrays (scipy.stats.mstats)
- scipy.stats.mstats.argstoarray
- scipy.stats.mstats.betai
- scipy.stats.mstats.chisquare
- scipy.stats.mstats.count_tied_groups
- scipy.stats.mstats.describe
- scipy.stats.mstats.f_oneway
- scipy.stats.mstats.f_value_wilks_lambda
- scipy.stats.mstats.find_repeats
- scipy.stats.mstats.friedmanchisquare
- scipy.stats.mstats.kendalltau
- scipy.stats.mstats.kendalltau_seasonal
- scipy.stats.mstats.kruskalwallis
- scipy.stats.mstats.ks_twosamp
- scipy.stats.mstats.kurtosis
- scipy.stats.mstats.kurtosistest
- scipy.stats.mstats.linregress
- scipy.stats.mstats.mannwhitneyu
- scipy.stats.mstats.plotting_positions
- scipy.stats.mstats.mode
- scipy.stats.mstats.moment
- scipy.stats.mstats.mquantiles
- scipy.stats.mstats.msign
- scipy.stats.mstats.normaltest
- scipy.stats.mstats.obrientransform
- scipy.stats.mstats.pearsonr
- scipy.stats.mstats.plotting_positions
- scipy.stats.mstats.pointbiserialr
- scipy.stats.mstats.rankdata
- scipy.stats.mstats.scoreatpercentile
- scipy.stats.mstats.sem
- scipy.stats.mstats.signaltonoise
- scipy.stats.mstats.skew
- scipy.stats.mstats.skewtest
- scipy.stats.mstats.spearmanr
- scipy.stats.mstats.theilslopes
- scipy.stats.mstats.threshold
- scipy.stats.mstats.tmax
- scipy.stats.mstats.tmean
- scipy.stats.mstats.tmin
- scipy.stats.mstats.trim
- scipy.stats.mstats.trima
- scipy.stats.mstats.trimboth
- scipy.stats.mstats.trimmed_stde
- scipy.stats.mstats.trimr
- scipy.stats.mstats.trimtail
- scipy.stats.mstats.tsem
- scipy.stats.mstats.ttest_onesamp
- scipy.stats.mstats.ttest_ind
- scipy.stats.mstats.ttest_onesamp
- scipy.stats.mstats.ttest_rel
- scipy.stats.mstats.tvar
- scipy.stats.mstats.variation
- scipy.stats.mstats.winsorize
- scipy.stats.mstats.zmap
- scipy.stats.mstats.zscore
Univariate and multivariate kernel density estimation (scipy.stats.kde)¶
| gaussian_kde(dataset[, bw_method]) | Representation of a kernel-density estimate using Gaussian kernels. |
For many more stat related functions install the software R and the interface package rpy.