Statistical functions (scipy.stats)

This module contains a large number of probability distributions as well as a growing library of statistical functions.

Each included continuous distribution is an instance of the class rv_continous:

rv_continuous A generic continuous random variable class meant for subclassing.
rv_continuous.pdf (self, x, *args, **kwds) Probability density function at x of the given RV.
rv_continuous.cdf (self, x, *args, **kwds) Cumulative distribution function at x of the given RV.
rv_continuous.sf (self, x, *args, **kwds) Survival function (1-cdf) at x of the given RV.
rv_continuous.ppf (self, q, *args, **kwds) Percent point function (inverse of cdf) at q of the given RV.
rv_continuous.isf (self, q, *args, **kwds) Inverse survival function at q of the given RV.
rv_continuous.stats (self, *args, **kwds) Some statistics of the given RV

Each discrete distribution is an instance of the class rv_discrete:

rv_discrete A generic discrete random variable class meant for subclassing.
rv_discrete.pmf (self, k, *args, **kwds) Probability mass function at k of the given RV.
rv_discrete.cdf (self, k, *args, **kwds) Cumulative distribution function at k of the given RV
rv_discrete.sf (self, k, *args, **kwds) Survival function (1-cdf) at k of the given RV
rv_discrete.ppf (self, q, *args, **kwds) Percent point function (inverse of cdf) at q of the given RV
rv_discrete.isf (self, q, *args, **kwds) Inverse survival function (1-sf) at q of the given RV
rv_discrete.stats (self, *args, **kwds) Some statistics of the given discrete RV

Continuous distributions

norm () A normal continuous random variable.
alpha () A alpha continuous random variable.
anglit () A anglit continuous random variable.
arcsine () A arcsine continuous random variable.
beta () A beta continuous random variable.
betaprime () A betaprime continuous random variable.
bradford () A Bradford continuous random variable.
burr () Burr continuous random variable.
fisk () A funk continuous random variable.
cauchy () 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.
fatiguelife () A fatigue-life (Birnbaum-Sanders) continuous random variable.
foldcauchy () A folded Cauchy continuous random variable.
f () An F continuous random variable.
foldnorm () A folded normal continuous random variable.
fretchet_r
fretcher_l
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.
gompertz () A Gompertz (truncated Gumbel) distribution 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.
invnorm () An inverse normal continuous random variable.
invweibull () An inverted Weibull continuous random variable.
johnsonsb () A Johnson SB continuous random variable.
johnsonsu () A Johnson SU continuous random variable.
laplace () A Laplace continuous random variable.
logistic () A logistic continuous random variable.
loggamma () A log gamma continuous random variable.
loglaplace () A log-Laplace continuous random variable.
lognorm () A lognormal continuous random variable.
gilbrat () A Gilbrat 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.
t () Student’s T continuous random variable.
nct () A Noncentral T continuous random variable.
pareto () A Pareto 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.
triang () A Triangular continuous random variable.
truncexpon () A truncated exponential continuous random variable.
truncnorm () A truncated normal continuous random variable.
tukeylambda () A Tukey-Lambda continuous random variable.
uniform () A uniform continuous random variable.
von_mises
wald () A Wald continuous random variable.
weibull_min () A Weibull minimum continuous random variable.
weibull_max () A Weibull maximum continuous random variable.
wrapcauchy () A wrapped Cauchy continuous random variable.
ksone () Kolmogorov-Smirnov A one-sided test statistic. continuous random variable.
kstwobign () Kolmogorov-Smirnov two-sided (for large N) continuous random variable.

Discrete distributions

binom () None discrete random variable.
bernoulli () None discrete random variable.
nbinom () A negative binomial discrete random variable.
geom () A geometric discrete random variable.
hypergeom () A hypergeometric discrete random variable.
logser () A logarithmic discrete random variable.
poisson () A Poisson discrete random variable.
planck () A discrete exponential discrete random variable.
boltzmann () A truncated discrete exponential discrete random variable.
randint () A discrete uniform (random integer) discrete random variable.
zipf () A Zipf discrete random variable.
dlaplace () A discrete Laplacian discrete random variable.

Statistical functions

Several of these functions have a similar version in scipy.stats.mstats which work for masked arrays.

gmean (a[, axis, dtype]) Compute the geometric mean along the specified axis.
hmean (a[, axis, dtype]) Calculates the harmonic mean along the specified axis.
mean (a[, axis]) Returns the arithmetic mean of m along the given dimension.
cmedian (a[, numbins]) Returns the computed median value of an array.
median (a[, axis]) Returns the median of the passed array along the given axis.
mode (a[, axis]) Returns an array of the modal (most common) value in the passed array.
tmean (a[, limits, inclusive, True)) Compute the trimmed mean
tvar (a[, limits, inclusive, 1)) Compute the trimmed variance
tmin (a[, lowerlimit, axis, ...]) Compute the trimmed minimum
tmax (a, upperlimit[, axis, inclusive]) Compute the trimmed maximum
tstd (a[, limits, inclusive, 1)) Compute the trimmed sample standard deviation
tsem (a[, limits, inclusive, True)) Compute the trimmed standard error of the mean
moment (a[, moment, axis]) Calculates the nth moment about the mean for a sample.
variation (a[, axis]) Computes the coefficient of variation, the ratio of the biased standard deviation to the mean.
skew (a[, axis, bias]) Computes the skewness of a data set.
kurtosis (a[, axis, fisher, bias]) Computes the kurtosis (Fisher or Pearson) of a dataset.
describe (a[, axis]) Computes several descriptive statistics of the passed array.
skewtest (a[, axis]) Tests whether the skew is different from the normal distribution.
kurtosistest (a[, axis]) Tests whether a dataset has normal kurtosis
normaltest (a[, axis]) Tests whether a sample differs from a normal distribution
itemfreq (a) Returns a 2D array of item frequencies.
scoreatpercentile (a, per[, limit=()) Calculate the score at the given ‘per’ percentile of the sequence a. For example, the score at per=50 is the median.
percentileofscore (a, score[, kind]) The percentile rank of a score relative to a list of scores.
histogram2 (a, bins) histogram2(a,bins) – Compute histogram of a using divisions in bins
histogram (a[, numbins, defaultlimits, ...]) Separates the range into several bins and returns the number of instances of a in each bin. This histogram is based on numpy’s histogram but has a larger range by default if default limits is not set.
cumfreq (a[, numbins, defaultreallimits, ...]) Returns a cumulative frequency histogram, using the histogram function. Defaultreallimits can be None (use all data), or a 2-sequence containing lower and upper limits on values to include.
relfreq (a[, numbins, defaultreallimits, ...]) Returns a relative frequency histogram, using the histogram function. Defaultreallimits can be None (use all data), or a 2-sequence containing lower and upper limits on values to include.
obrientransform (*args) Computes a transform on input data (any number of columns). Used to test for homogeneity of variance prior to running one-way stats. Each array in *args is one level of a factor. If an F_oneway() run on the transformed data and found significant, variances are unequal. From Maxwell and Delaney, p.112.
samplevar (*args, **kwds) samplevar is deprecated!
samplestd (*args, **kwds) samplestd is deprecated!
signaltonoise (a[, axis, ddof]) Calculates the signal-to-noise ratio, defined as the ratio between the mean and the standard deviation.
bayes_mvs (data[, alpha]) Return Bayesian confidence intervals for the mean, var, and std.
var (a[, axis, bias]) Returns the estimated population variance of the values in the passed array (i.e., N-1). Axis can equal None (ravel array first), or an integer (the axis over which to operate).
std (a[, axis, bias]) Returns the estimated population standard deviation of the values in the passed array (i.e., N-1). Axis can equal None (ravel array first), or an integer (the axis over which to operate).
stderr (*args, **kwds) stderr is deprecated!
sem (a[, axis, ddof]) Calculates the standard error of the mean (or standard error of measurement) of the values in the passed array.
z (*args, **kwds) z is deprecated!
zs (*args, **kwds) zs is deprecated!
zmap (scores, compare[, axis]) Returns an array of z-scores the shape of scores (e.g., [x,y]), compared to array passed to compare (e.g., [time,x,y]). Assumes collapsing over dim 0 of the compare array.
threshold (a[, threshmin, threshmax, ...]) Clip array to a given value.
trimboth (a, proportiontocut) Slices off the passed proportion of items from BOTH ends of the passed array (i.e., with proportiontocut=0.1, slices ‘leftmost’ 10% AND ‘rightmost’ 10% of scores. You must pre-sort the array if you want “proper” trimming. Slices off LESS if proportion results in a non-integer slice index (i.e., conservatively slices off proportiontocut).
trim1 (a, proportiontocut[, tail]) Slices off the passed proportion of items from ONE end of the passed array (i.e., if proportiontocut=0.1, slices off ‘leftmost’ or ‘rightmost’ 10% of scores). Slices off LESS if proportion results in a non-integer slice index (i.e., conservatively slices off proportiontocut).
cov (m[, y, rowvar, bias]) Estimate the covariance matrix.
corrcoef (x[, y, rowvar, bias]) The correlation coefficients formed from 2-d array x, where the rows are the observations, and the columns are variables.
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) Calculates Kendall’s tau, a correlation measure for ordinal data
linregress (*args) Calculate a regression line
ttest_1samp (a, popmean[, axis]) Calculates the T-test for the mean of ONE group of scores a.
ttest_ind (a, b[, axis]) 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, **kwds) Perform the Kolmogorov-Smirnov test for goodness of fit
chisquare (f_obs[, f_exp, ddof]) Calculates a one-way chi square test.
ks_2samp (data1, data2) Computes the Kolmogorov-Smirnof statistic on 2 samples.
mannwhitneyu (x, y[, use_continuity]) Computes the Mann-Whitney rank test on samples x and y.
tiecorrect (rankvals) Tie-corrector for ties in Mann Whitney U and Kruskal Wallis H tests. See Siegel, S. (1956) Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill. Code adapted from |Stat rankind.c code.
ranksums (x, y) Compute the Wilcoxon rank-sum statistic for two samples.
wilcoxon (x[, y]) 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
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
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
mood (x, y) Perform Mood’s test for equal scale parameters
oneway (*args, **kwds) Test for equal means in two or more samples from the normal distribution.
glm (data, para) Calculates a linear model fit ... anova/ancova/lin-regress/t-test/etc. Taken from:
anova

Plot-tests

probplot (x[, sparams=(), dist, ...]) Return (osm, osr){,(scale,loc,r)} where (osm, osr) are order statistic medians and ordered response data respectively so that plot(osm, osr) is a probability plot. If fit==1, then do a regression fit and compute the slope (scale), intercept (loc), and correlation coefficient (r), of the best straight line through the points. If fit==0, only (osm, osr) is returned.
ppcc_max (x[, brack, 1.0), 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. ppcc (probability plot correlation coefficient) as a function of shape parameter for a one-parameter family of distributions from shape value a to b.

Masked statistics functions

Univariate and multivariate kernel density estimation (scipy.stats.kde)

gaussian_kde Representation of a kernel-density estimate using Gaussian kernels.

For many more stat related functions install the software R and the interface package rpy.