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.
PyMC: 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):
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A generic continuous random variable class meant for subclassing. |
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A generic discrete random variable class meant for subclassing. |
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Generates a distribution given by a histogram. |
Continuous distributions#
An alpha continuous random variable. |
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An anglit continuous random variable. |
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An arcsine continuous random variable. |
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Argus distribution |
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A beta continuous random variable. |
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A beta prime continuous random variable. |
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A Bradford continuous random variable. |
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A Burr (Type III) continuous random variable. |
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A Burr (Type XII) continuous random variable. |
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A Cauchy continuous random variable. |
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A chi continuous random variable. |
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A chi-squared continuous random variable. |
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A cosine continuous random variable. |
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Crystalball distribution |
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A double gamma continuous random variable. |
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A double Pareto lognormal continuous random variable. |
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A double Weibull continuous random variable. |
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An Erlang continuous random variable. |
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An exponential continuous random variable. |
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An exponentially modified Normal continuous random variable. |
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An exponentiated Weibull continuous random variable. |
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An exponential power continuous random variable. |
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An F continuous random variable. |
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A fatigue-life (Birnbaum-Saunders) continuous random variable. |
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A Fisk continuous random variable. |
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A folded Cauchy continuous random variable. |
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A folded normal continuous random variable. |
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A generalized logistic continuous random variable. |
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A generalized normal continuous random variable. |
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A generalized Pareto continuous random variable. |
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A generalized exponential continuous random variable. |
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A generalized extreme value continuous random variable. |
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A Gauss hypergeometric continuous random variable. |
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A gamma continuous random variable. |
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A generalized gamma continuous random variable. |
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A generalized half-logistic continuous random variable. |
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A generalized hyperbolic continuous random variable. |
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A Generalized Inverse Gaussian continuous random variable. |
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A Gibrat continuous random variable. |
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A Gompertz (or truncated Gumbel) continuous random variable. |
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A right-skewed Gumbel continuous random variable. |
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A left-skewed Gumbel continuous random variable. |
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A Half-Cauchy continuous random variable. |
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A half-logistic continuous random variable. |
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A half-normal continuous random variable. |
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The upper half of a generalized normal continuous random variable. |
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A hyperbolic secant continuous random variable. |
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An inverted gamma continuous random variable. |
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An inverse Gaussian continuous random variable. |
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An inverted Weibull continuous random variable. |
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An Irwin-Hall (Uniform Sum) continuous random variable. |
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Jones and Faddy skew-t distribution. |
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A Johnson SB continuous random variable. |
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A Johnson SU continuous random variable. |
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Kappa 4 parameter distribution. |
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Kappa 3 parameter distribution. |
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Kolmogorov-Smirnov one-sided test statistic distribution. |
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Kolmogorov-Smirnov two-sided test statistic distribution. |
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Limiting distribution of scaled Kolmogorov-Smirnov two-sided test statistic. |
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A Landau continuous random variable. |
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A Laplace continuous random variable. |
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An asymmetric Laplace continuous random variable. |
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A Levy continuous random variable. |
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A left-skewed Levy continuous random variable. |
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A Levy-stable continuous random variable. |
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A logistic (or Sech-squared) continuous random variable. |
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A log gamma continuous random variable. |
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A log-Laplace continuous random variable. |
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A lognormal continuous random variable. |
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A loguniform or reciprocal continuous random variable. |
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A Lomax (Pareto of the second kind) continuous random variable. |
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A Maxwell continuous random variable. |
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A Mielke Beta-Kappa / Dagum continuous random variable. |
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A Moyal continuous random variable. |
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A Nakagami continuous random variable. |
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A non-central chi-squared continuous random variable. |
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A non-central F distribution continuous random variable. |
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A non-central Student's t continuous random variable. |
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A normal continuous random variable. |
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A Normal Inverse Gaussian continuous random variable. |
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A Pareto continuous random variable. |
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A pearson type III continuous random variable. |
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A power-function continuous random variable. |
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A power log-normal continuous random variable. |
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A power normal continuous random variable. |
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An R-distributed (symmetric beta) continuous random variable. |
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A Rayleigh continuous random variable. |
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A relativistic Breit-Wigner random variable. |
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A Rice continuous random variable. |
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A reciprocal inverse Gaussian continuous random variable. |
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A semicircular continuous random variable. |
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A skewed Cauchy random variable. |
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A skew-normal random variable. |
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A studentized range continuous random variable. |
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A Student's t continuous random variable. |
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A trapezoidal continuous random variable. |
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A triangular continuous random variable. |
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A truncated exponential continuous random variable. |
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A truncated normal continuous random variable. |
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An upper truncated Pareto continuous random variable. |
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A doubly truncated Weibull minimum continuous random variable. |
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A Tukey-Lamdba continuous random variable. |
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A uniform continuous random variable. |
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A Von Mises continuous random variable. |
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A Von Mises continuous random variable. |
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A Wald continuous random variable. |
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Weibull minimum continuous random variable. |
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Weibull maximum continuous random variable. |
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A wrapped Cauchy continuous random variable. |
The fit
method of the univariate continuous distributions uses
maximum likelihood estimation to fit the distribution to a data set.
The fit
method can accept regular data or censored data.
Censored data is represented with instances of the CensoredData
class.
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Instances of this class represent censored data. |
Multivariate distributions#
A multivariate normal random variable. |
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A matrix normal random variable. |
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A Dirichlet random variable. |
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A Dirichlet multinomial random variable. |
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A Wishart random variable. |
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An inverse Wishart random variable. |
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A multinomial random variable. |
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A Special Orthogonal matrix (SO(N)) random variable. |
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An Orthogonal matrix (O(N)) random variable. |
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A matrix-valued U(N) random variable. |
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A random correlation matrix. |
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A multivariate t-distributed random variable. |
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A multivariate hypergeometric random variable. |
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Normal-inverse-gamma distribution. |
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Contingency tables from independent samples with fixed marginal sums. |
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A vector-valued uniform direction. |
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A von Mises-Fisher variable. |
scipy.stats.multivariate_normal
methods accept instances
of the following class to represent the covariance.
Representation of a covariance matrix |
Discrete distributions#
A Bernoulli discrete random variable. |
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A beta-binomial discrete random variable. |
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A beta-negative-binomial discrete random variable. |
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A binomial discrete random variable. |
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A Boltzmann (Truncated Discrete Exponential) random variable. |
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A Laplacian discrete random variable. |
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A geometric discrete random variable. |
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A hypergeometric discrete random variable. |
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A Logarithmic (Log-Series, Series) discrete random variable. |
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A negative binomial discrete random variable. |
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A Fisher's noncentral hypergeometric discrete random variable. |
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A Wallenius' noncentral hypergeometric discrete random variable. |
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A negative hypergeometric discrete random variable. |
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A Planck discrete exponential random variable. |
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A Poisson discrete random variable. |
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A Poisson Binomial discrete random variable. |
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A uniform discrete random variable. |
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A Skellam discrete random variable. |
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A Yule-Simon discrete random variable. |
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A Zipf (Zeta) discrete random variable. |
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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#
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Compute several descriptive statistics of the passed array. |
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Compute the weighted geometric mean along the specified axis. |
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Calculate the weighted harmonic mean along the specified axis. |
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Calculate the weighted power mean along the specified axis. |
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Compute the kurtosis (Fisher or Pearson) of a dataset. |
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Return an array of the modal (most common) value in the passed array. |
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Calculate the nth moment about the mean for a sample. |
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Compute L-moments of a sample from a continuous distribution |
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Compute the expectile at the specified level. |
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Compute the sample skewness of a data set. |
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Return the n th k-statistic ( |
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Return an unbiased estimator of the variance of the k-statistic. |
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Compute the trimmed mean. |
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Compute the trimmed variance. |
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Compute the trimmed minimum. |
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Compute the trimmed maximum. |
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Compute the trimmed sample standard deviation. |
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Compute the trimmed standard error of the mean. |
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Compute the coefficient of variation. |
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Find repeats and repeat counts. |
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Assign ranks to data, dealing with ties appropriately. |
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Tie correction factor for Mann-Whitney U and Kruskal-Wallis H tests. |
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Return mean of array after trimming a specified fraction of extreme values |
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Calculate the geometric standard deviation of an array. |
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Compute the interquartile range of the data along the specified axis. |
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Compute standard error of the mean. |
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Bayesian confidence intervals for the mean, var, and std. |
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'Frozen' distributions for mean, variance, and standard deviation of data. |
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Calculate the Shannon entropy/relative entropy of given distribution(s). |
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Given a sample of a distribution, estimate the differential entropy. |
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Compute the median absolute deviation of the data along the given axis. |
Frequency statistics#
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Return a cumulative frequency histogram, using the histogram function. |
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Compute the percentile rank of a score relative to a list of scores. |
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Calculate the score at a given percentile of the input sequence. |
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Return a relative frequency histogram, using the histogram function. |
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Compute a binned statistic for one or more sets of data. |
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Compute a bidimensional binned statistic for one or more sets of data. |
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Compute a multidimensional binned statistic for a set of data. |
Random Variables#
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Generate a ContinuousDistribution from an instance of |
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Normal distribution with prescribed mean and standard deviation. |
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Uniform distribution. |
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Representation of a mixture distribution. |
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Probability distribution of an order statistic |
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Truncate the support of a random variable. |
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Absolute value of a random variable |
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Natural exponential of a random variable |
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Natural logarithm of a non-negative random variable |
Quasi-Monte Carlo#
Contingency Tables#
Masked statistics functions#
- Statistical functions for masked arrays (
scipy.stats.mstats
)- Summary statistics
- Frequency statistics
- Correlation functions
- Statistical tests
- Transformations
- Other
Other statistical functionality#
Transformations#
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Return a dataset transformed by a Box-Cox power transformation. |
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Compute optimal Box-Cox transform parameter for input data. |
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The boxcox log-likelihood function. |
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Return a dataset transformed by a Yeo-Johnson power transformation. |
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Compute optimal Yeo-Johnson transform parameter. |
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The yeojohnson log-likelihood function. |
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Compute the O'Brien transform on input data (any number of arrays). |
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Perform iterative sigma-clipping of array elements. |
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Slice off a proportion of items from both ends of an array. |
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Slice off a proportion from ONE end of the passed array distribution. |
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Calculate the relative z-scores. |
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Compute the z score. |
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Compute the geometric standard score. |
Statistical distances#
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Compute the Wasserstein-1 distance between two 1D discrete distributions. |
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Compute the Wasserstein-1 distance between two N-D discrete distributions. |
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Compute the energy distance between two 1D distributions. |
Sampling#
Fitting / Survival Analysis#
Directional statistical functions#
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Computes sample statistics for directional data. |
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Compute the circular mean of a sample of angle observations. |
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Compute the circular variance of a sample of angle observations. |
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Compute the circular standard deviation of a sample of angle observations. |
Sensitivity Analysis#
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Global sensitivity indices of Sobol'. |
Plot-tests#
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Calculate the shape parameter that maximizes the PPCC. |
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Calculate and optionally plot probability plot correlation coefficient. |
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Calculate quantiles for a probability plot, and optionally show the plot. |
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Compute parameters for a Box-Cox normality plot, optionally show it. |
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Compute parameters for a Yeo-Johnson normality plot, optionally show it. |
Univariate and multivariate kernel density estimation#
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Representation of a kernel-density estimate using Gaussian kernels. |
Warnings / Errors used in scipy.stats
#
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Warns when data is degenerate and results may not be reliable. |
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Warns when all values in data are exactly equal. |
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Warns when all values in data are nearly equal. |
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Represents an error condition when fitting a distribution to data. |
Result classes used in scipy.stats
#
Warning
These classes are private, but they are included here because instances of them are returned by other statistical functions. User import and instantiation is not supported.