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bundles / scipy 1.17.1 / scipy / stats

module

scipy.stats

source: /scipy/stats/__init__.py :0

Submodules

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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):

.. autosummary:: 
    :toctree:generated/
    rv_continuous
    rv_discrete
    rv_histogram

Continuous distributions

.. autosummary:: 
    :toctree:generated/
    alpha             -- Alpha
    anglit            -- Anglit
    arcsine           -- Arcsine
    argus             -- Argus
    beta              -- Beta
    betaprime         -- Beta Prime
    bradford          -- Bradford
    burr              -- Burr (Type III)
    burr12            -- Burr (Type XII)
    cauchy            -- Cauchy
    chi               -- Chi
    chi2              -- Chi-squared
    cosine            -- Cosine
    crystalball       -- Crystalball
    dgamma            -- Double Gamma
    dpareto_lognorm   -- Double Pareto Lognormal
    dweibull          -- Double Weibull
    erlang            -- Erlang
    expon             -- Exponential
    exponnorm         -- Exponentially Modified Normal
    exponweib         -- Exponentiated Weibull
    exponpow          -- Exponential Power
    f                 -- F (Snecdor F)
    fatiguelife       -- Fatigue Life (Birnbaum-Saunders)
    fisk              -- Fisk
    foldcauchy        -- Folded Cauchy
    foldnorm          -- Folded Normal
    genlogistic       -- Generalized Logistic
    gennorm           -- Generalized normal
    genpareto         -- Generalized Pareto
    genexpon          -- Generalized Exponential
    genextreme        -- Generalized Extreme Value
    gausshyper        -- Gauss Hypergeometric
    gamma             -- Gamma
    gengamma          -- Generalized gamma
    genhalflogistic   -- Generalized Half Logistic
    genhyperbolic     -- Generalized Hyperbolic
    geninvgauss       -- Generalized Inverse Gaussian
    gibrat            -- Gibrat
    gompertz          -- Gompertz (Truncated Gumbel)
    gumbel_r          -- Right Sided Gumbel, Log-Weibull, Fisher-Tippett, Extreme Value Type I
    gumbel_l          -- Left Sided Gumbel, etc.
    halfcauchy        -- Half Cauchy
    halflogistic      -- Half Logistic
    halfnorm          -- Half Normal
    halfgennorm       -- Generalized Half Normal
    hypsecant         -- Hyperbolic Secant
    invgamma          -- Inverse Gamma
    invgauss          -- Inverse Gaussian
    invweibull        -- Inverse Weibull
    irwinhall         -- Irwin-Hall
    jf_skew_t         -- Jones and Faddy Skew-T
    johnsonsb         -- Johnson SB
    johnsonsu         -- Johnson SU
    kappa4            -- Kappa 4 parameter
    kappa3            -- Kappa 3 parameter
    ksone             -- Distribution of Kolmogorov-Smirnov one-sided test statistic
    kstwo             -- Distribution of Kolmogorov-Smirnov two-sided test statistic
    kstwobign         -- Limiting Distribution of scaled Kolmogorov-Smirnov two-sided test statistic.
    landau            -- Landau
    laplace           -- Laplace
    laplace_asymmetric    -- Asymmetric Laplace
    levy              -- Levy
    levy_l
    levy_stable
    logistic          -- Logistic
    loggamma          -- Log-Gamma
    loglaplace        -- Log-Laplace (Log Double Exponential)
    lognorm           -- Log-Normal
    loguniform        -- Log-Uniform
    lomax             -- Lomax (Pareto of the second kind)
    maxwell           -- Maxwell
    mielke            -- Mielke's Beta-Kappa
    moyal             -- Moyal
    nakagami          -- Nakagami
    ncx2              -- Non-central chi-squared
    ncf               -- Non-central F
    nct               -- Non-central Student's T
    norm              -- Normal (Gaussian)
    norminvgauss      -- Normal Inverse Gaussian
    pareto            -- Pareto
    pearson3          -- Pearson type III
    powerlaw          -- Power-function
    powerlognorm      -- Power log normal
    powernorm         -- Power normal
    rdist             -- R-distribution
    rayleigh          -- Rayleigh
    rel_breitwigner   -- Relativistic Breit-Wigner
    rice              -- Rice
    recipinvgauss     -- Reciprocal Inverse Gaussian
    semicircular      -- Semicircular
    skewcauchy        -- Skew Cauchy
    skewnorm          -- Skew normal
    studentized_range    -- Studentized Range
    t                 -- Student's T
    trapezoid         -- Trapezoidal
    triang            -- Triangular
    truncexpon        -- Truncated Exponential
    truncnorm         -- Truncated Normal
    truncpareto       -- Truncated Pareto
    truncweibull_min  -- Truncated minimum Weibull distribution
    tukeylambda       -- Tukey-Lambda
    uniform           -- Uniform
    vonmises          -- Von-Mises (Circular)
    vonmises_line     -- Von-Mises (Line)
    wald              -- Wald
    weibull_min       -- Minimum Weibull (see Frechet)
    weibull_max       -- Maximum Weibull (see Frechet)
    wrapcauchy        -- Wrapped Cauchy

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.

.. autosummary:: 
    :toctree:generated/
    CensoredData

Multivariate distributions

.. autosummary:: 
    :toctree:generated/
    multivariate_normal    -- Multivariate normal distribution
    matrix_normal          -- Matrix normal distribution
    dirichlet              -- Dirichlet
    dirichlet_multinomial  -- Dirichlet multinomial distribution
    wishart                -- Wishart
    invwishart             -- Inverse Wishart
    multinomial            -- Multinomial distribution
    special_ortho_group    -- SO(N) group
    ortho_group            -- O(N) group
    unitary_group          -- U(N) group
    random_correlation     -- random correlation matrices
    multivariate_t         -- Multivariate t-distribution
    multivariate_hypergeom -- Multivariate hypergeometric distribution
    normal_inverse_gamma   -- Normal-inverse-gamma distribution
    random_table           -- Distribution of random tables with given marginals
    uniform_direction      -- Uniform distribution on S(N-1)
    vonmises_fisher        -- Von Mises-Fisher distribution
    matrix_t               -- Matrix variate t distribution

scipy.stats.multivariate_normal methods accept instances of the following class to represent the covariance.

.. autosummary:: 
    :toctree:generated/
    Covariance             -- Representation of a covariance matrix

Discrete distributions

.. autosummary:: 
    :toctree:generated/
    bernoulli                -- Bernoulli
    betabinom                -- Beta-Binomial
    betanbinom               -- Beta-Negative Binomial
    binom                    -- Binomial
    boltzmann                -- Boltzmann (Truncated Discrete Exponential)
    dlaplace                 -- Discrete Laplacian
    geom                     -- Geometric
    hypergeom                -- Hypergeometric
    logser                   -- Logarithmic (Log-Series, Series)
    nbinom                   -- Negative Binomial
    nchypergeom_fisher       -- Fisher's Noncentral Hypergeometric
    nchypergeom_wallenius    -- Wallenius's Noncentral Hypergeometric
    nhypergeom               -- Negative Hypergeometric
    planck                   -- Planck (Discrete Exponential)
    poisson                  -- Poisson
    poisson_binom            -- Poisson Binomial
    randint                  -- Discrete Uniform
    skellam                  -- Skellam
    yulesimon                -- Yule-Simon
    zipf                     -- Zipf (Zeta)
    zipfian                  -- Zipfian

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

.. autosummary:: 
    :toctree:generated/
    describe          -- Descriptive statistics
    gmean             -- Geometric mean
    hmean             -- Harmonic mean
    pmean             -- Power mean
    kurtosis          -- Fisher or Pearson kurtosis
    mode              -- Modal value
    moment            -- Central moment
    lmoment
    expectile         -- Expectile
    skew              -- Skewness
    kstat             --
    kstatvar          --
    tmean             -- Truncated arithmetic mean
    tvar              -- Truncated variance
    tmin              --
    tmax              --
    tstd              --
    tsem              --
    variation         -- Coefficient of variation
    rankdata
    tiecorrect
    trim_mean
    gstd              -- Geometric Standard Deviation
    iqr
    sem
    bayes_mvs
    mvsdist
    entropy
    differential_entropy
    median_abs_deviation

Frequency statistics

.. autosummary:: 
    :toctree:generated/
    cumfreq
    quantile
    percentileofscore
    scoreatpercentile
    relfreq
.. autosummary:: 
    :toctree:generated/
    binned_statistic     -- Compute a binned statistic for a set of data.
    binned_statistic_2d  -- Compute a 2-D binned statistic for a set of data.
    binned_statistic_dd  -- Compute a d-D binned statistic for a set of data.

Hypothesis Tests and related functions

SciPy has many functions for performing hypothesis tests that return a test statistic and a p-value, and several of them return confidence intervals and/or other related information.

The headings below are based on common uses of the functions within, but due to the wide variety of statistical procedures, any attempt at coarse-grained categorization will be imperfect. Also, note that tests within the same heading are not interchangeable in general (e.g. many have different distributional assumptions).

One Sample Tests / Paired Sample Tests

One sample tests are typically used to assess whether a single sample was drawn from a specified distribution or a distribution with specified properties (e.g. zero mean).

.. autosummary:: 
    :toctree:generated/
    ttest_1samp
    binomtest
    quantile_test
    skewtest
    kurtosistest
    normaltest
    jarque_bera
    shapiro
    anderson
    cramervonmises
    ks_1samp
    goodness_of_fit
    chisquare
    power_divergence

Paired sample tests are often used to assess whether two samples were drawn from the same distribution; they differ from the independent sample tests below in that each observation in one sample is treated as paired with a closely-related observation in the other sample (e.g. when environmental factors are controlled between observations within a pair but not among pairs). They can also be interpreted or used as one-sample tests (e.g. tests on the mean or median of differences between paired observations).

.. autosummary:: 
    :toctree:generated/
    ttest_rel
    wilcoxon

Association/Correlation Tests

These tests are often used to assess whether there is a relationship (e.g. linear) between paired observations in multiple samples or among the coordinates of multivariate observations.

.. autosummary:: 
    :toctree:generated/
    linregress
    pearsonr
    spearmanrho
    pointbiserialr
    kendalltau
    chatterjeexi
    weightedtau
    somersd
    siegelslopes
    theilslopes
    page_trend_test
    multiscale_graphcorr
    spearmanr

These association tests and are to work with samples in the form of contingency tables. Supporting functions are available in scipy.stats.contingency.

.. autosummary:: 
    :toctree:generated/
    chi2_contingency
    fisher_exact
    barnard_exact
    boschloo_exact

Independent Sample Tests

Independent sample tests are typically used to assess whether multiple samples were independently drawn from the same distribution or different distributions with a shared property (e.g. equal means).

Some tests are specifically for comparing two samples.

.. autosummary:: 
    :toctree:generated/
    ttest_ind_from_stats
    poisson_means_test
    ttest_ind
    mannwhitneyu
    bws_test
    ranksums
    brunnermunzel
    mood
    ansari
    cramervonmises_2samp
    epps_singleton_2samp
    ks_2samp
    kstest

Others are generalized to multiple samples.

.. autosummary:: 
    :toctree:generated/
    f_oneway
    tukey_hsd
    dunnett
    kruskal
    alexandergovern
    fligner
    levene
    bartlett
    median_test
    friedmanchisquare
    anderson_ksamp

Resampling and Monte Carlo Methods

The following functions can reproduce the p-value and confidence interval results of most of the functions above, and often produce accurate results in a wider variety of conditions. They can also be used to perform hypothesis tests and generate confidence intervals for custom statistics. This flexibility comes at the cost of greater computational requirements and stochastic results.

.. autosummary:: 
    :toctree:generated/
    monte_carlo_test
    permutation_test
    bootstrap
    power

Instances of the following object can be passed into some hypothesis test functions to perform a resampling or Monte Carlo version of the hypothesis test.

.. autosummary:: 
    :toctree:generated/
    MonteCarloMethod
    PermutationMethod
    BootstrapMethod

Multiple Hypothesis Testing and Meta-Analysis

These functions are for assessing the results of individual tests as a whole. Functions for performing specific multiple hypothesis tests (e.g. post hoc tests) are listed above.

.. autosummary:: 
    :toctree:generated/
    combine_pvalues
    false_discovery_control

The following functions are related to the tests above but do not belong in the above categories.

Random Variables

.. autosummary:: 
    :toctree:generated/
    make_distribution
    Normal
    Logistic
    Uniform
    Binomial
    Mixture
    order_statistic
    truncate
    abs
    exp
    log

Quasi-Monte Carlo

Contingency Tables

Masked statistics functions

Other statistical functionality

Transformations

.. autosummary:: 
    :toctree:generated/
    boxcox
    boxcox_normmax
    boxcox_llf
    yeojohnson
    yeojohnson_normmax
    yeojohnson_llf
    obrientransform
    sigmaclip
    trimboth
    trim1
    zmap
    zscore
    gzscore

Statistical distances

.. autosummary:: 
    :toctree:generated/
    wasserstein_distance
    wasserstein_distance_nd
    energy_distance

Sampling

Fitting / Survival Analysis

.. autosummary:: 
    :toctree:generated/
    fit
    ecdf
    logrank

Directional statistical functions

.. autosummary:: 
    :toctree:generated/
    directional_stats
    circmean
    circvar
    circstd

Sensitivity Analysis

.. autosummary:: 
    :toctree:generated/
    sobol_indices

Plot-tests

.. autosummary:: 
    :toctree:generated/
    ppcc_max
    ppcc_plot
    probplot
    boxcox_normplot
    yeojohnson_normplot

Univariate and multivariate kernel density estimation

.. autosummary:: 
    :toctree:generated/
    gaussian_kde

Warnings / Errors used in scipy.stats

.. autosummary:: 
    :toctree:generated/
    DegenerateDataWarning
    ConstantInputWarning
    NearConstantInputWarning
    FitError

Result classes used in scipy.stats

Aliases

  • scipy.stats

Referenced by

This package