API reference

The scientific categories below follow the order used by the SHT reference. The public API contains 51 canonical pySHT functions covering 52 of the 54 statistical routine identities in SHT 0.1.9. Two one-sample mean-and-variance identities share one algebraically identical implementation; mean2.2014CLX remains a private validation target after failing its practical-size calibration gate, and cov1.2012Fisher is withheld because its release audit is not reproducible. Every public Python function uses lowercase snake_case and lives in its subject module; test functions are not re-exported by pysht.

[0] Utilities

SHT’s dynamic usek1d and useknd adapters have no direct pySHT counterpart. Python functions can be passed and called directly.

[1] Tests for Univariate Mean

Function	Purpose
pysht.mean.ttest_1samp	Test one population mean against a reference value
pysht.mean.ttest_2samp	Compare two independent or paired population means
pysht.mean.anova_oneway	Compare means across two or more independent groups

[2] Tests for Multivariate Mean

Function	Purpose
pysht.mean.hotelling_1samp	One-sample Hotelling mean-vector test
pysht.mean.hotelling_2samp	Independent or paired Hotelling mean-vector test
pysht.mean.dempster_1samp	One-sample Dempster test
pysht.mean.bs_1samp	One-sample Bai–Saranadasa test
pysht.mean.sd_1samp	One-sample Srivastava–Du test
pysht.mean.dempster_2samp	Two-sample Dempster test
pysht.mean.yao_2samp	Yao unequal-covariance test
pysht.mean.johansen_2samp	Johansen unequal-covariance test
pysht.mean.nvm_2samp	Nel–Van der Merwe unequal-covariance test
pysht.mean.bs_2samp	Two-sample Bai–Saranadasa test
pysht.mean.ky_2samp	Krishnamoorthy–Yu unequal-covariance test
pysht.mean.sd_2samp	Two-sample Srivastava–Du test
pysht.mean.ljw_2samp	Lopes–Jacob–Wainwright random-projection test
pysht.mean.thulin_2samp	Thulin random-subspace test
pysht.mean.lyl_2samp	Lee–You–Lin maximum log Bayes-factor test
pysht.mean.schott_ksamp	Schott multi-sample mean test
pysht.mean.zx_ksamp	Zhang–Xu transformed multi-sample test
pysht.mean.cph_ksamp	Cao–Park–He high-dimensional multi-sample test

[3] Tests for Variance

Function	Purpose
pysht.variance.chisquare_1samp	Test one population variance against a reference value
pysht.variance.f_2samp	Compare two normal-population variances
pysht.variance.bartlett	Compare variances across normal populations
pysht.variance.levene	Compare group spreads around their means
pysht.variance.brown_forsythe	Compare group spreads around their medians

[4] Tests for Covariance

Function	Purpose
pysht.covariance.wl_1samp	Random-projection one-sample covariance test
pysht.covariance.lc_2samp	Li–Chen two-sample covariance test
pysht.covariance.clx_2samp	Cai–Liu–Xia maximum covariance test
pysht.covariance.wl_2samp	Random-projection two-sample covariance test
pysht.covariance.lyl_2samp	Lee–You–Lin known-zero-mean maximum log Bayes-factor test
pysht.covariance.schott_2001_ksamp	Schott (2001) multi-sample covariance test
pysht.covariance.schott_2007_ksamp	Schott (2007) high-dimensional multi-sample test

[5] Simultaneous Tests for Mean and Variance

Function	Purpose
pysht.mean_variance.as_1samp	Test one normal mean and variance jointly
pysht.mean_variance.pn_2samp	Pearson–Neyman two-sample joint test
pysht.mean_variance.pl_2samp	Perng–Littell component-test combination
pysht.mean_variance.muirhead_2samp	Muirhead corrected likelihood-ratio approximation
pysht.mean_variance.zxc_2samp	Zhang–Xu–Chen exact likelihood-ratio calibration
pysht.mean_variance.lrt_2samp	Asymptotic two-sample likelihood-ratio test

[6] Simultaneous Tests for Mean and Covariance

Function	Purpose
pysht.mean_covariance.llzs_1samp	Liu–Liu–Zheng–Shi high-dimensional one-sample test
pysht.mean_covariance.lrt_1samp	Classical one-sample likelihood-ratio test
pysht.mean_covariance.hn_2samp	Hyodo–Nishiyama high-dimensional two-sample test

[7] Tests for Equality of Distributions

Function	Purpose
pysht.equaldist.bg_2samp	Compare two univariate or multivariate distributions

[8] Goodness-of-Fit: Normal Distribution

Function	Purpose
pysht.normality.shapiro_wilk	Shapiro–Wilk normality test
pysht.normality.shapiro_francia	Shapiro–Francia normality test
pysht.normality.jarque_bera	Jarque–Bera moment test
pysht.normality.adjusted_jarque_bera	Adjusted Jarque–Bera moment test
pysht.normality.robust_jarque_bera	Robust Jarque–Bera moment test

[9] Goodness-of-Fit: Uniform Distribution

Function	Purpose
pysht.uniformity.ym_interpoint	Yang–Modarres interpoint-distance test
pysht.uniformity.ym_quantile	Yang–Modarres normal-quantile test

[10] Tests on Special Domains

Function	Purpose
pysht.simplex.uniformity	Likelihood-ratio test of probability-simplex uniformity

Result objects

Every public test returns an immutable StatisticalTestResult subtype. Frequentist tests report an htest-style statistic and p-value; resampling results add exactness and Monte Carlo diagnostics. The two Lee–You–Lin functions instead return a maximum log Bayes factor and have no p-value.

For R names, years, and expanded author acronyms, use the migration crosswalk and searchable method-name glossary.