API reference

Categories [0]–[10] preserve the order used by the SHT reference. Categories [11]–[12] contain pySHT-native independence and circular-data methods. The R crosswalk remains limited to SHT identities; native additions have their own catalog. The candidate catalog contains 72 canonical public functions, including 21 validated pySHT-native additions. Every public function uses lowercase snake_case, lives in its scientific module, and is not re-exported from top-level pysht.

[0] Utilities

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

[1] Tests for Univariate Mean

Function	Purpose
pysht.mean.ttest_1samp	One population mean
pysht.mean.ttest_2samp	Two independent or paired means
pysht.mean.anova_oneway	Two or more independent means

[2] Tests for Multivariate Mean

Function	Purpose
pysht.mean.hotelling_1samp	One-sample Hotelling test
pysht.mean.hotelling_2samp	Independent or paired Hotelling test
pysht.mean.dempster_1samp, dempster_2samp	Dempster mean tests
pysht.mean.bs_1samp, bs_2samp	Bai–Saranadasa tests
pysht.mean.sd_1samp, sd_2samp	Srivastava–Du tests
pysht.mean.yao_2samp	Yao unequal-covariance test
pysht.mean.johansen_2samp	Johansen unequal-covariance test
pysht.mean.nvm_2samp	Nel–Van der Merwe test
pysht.mean.ky_2samp	Krishnamoorthy–Yu test
pysht.mean.ljw_2samp	Random-projection test
pysht.mean.thulin_2samp	Random-subspace test
pysht.mean.cq_2samp	Chen–Qin dense high-dimensional test
pysht.mean.li_1samp, li_2samp, li_ksamp	Li fixed-small-sample tests
pysht.mean.maximum_pairwise_bayes_factor_2samp	Lee–You–Lin maximum pairwise log Bayes factor
pysht.mean.schott_ksamp	Schott multi-sample test
pysht.mean.zx_ksamp	Zhang–Xu transformed test
pysht.mean.cph_ksamp	Cao–Park–He test

[3] Tests for Variance

Function	Purpose
pysht.variance.chisquare_1samp	One normal-population variance
pysht.variance.f_2samp	Two normal-population variances
pysht.variance.bartlett	Normal-population variance homogeneity
pysht.variance.levene	Spread around group means
pysht.variance.brown_forsythe	Spread around group medians

[4] Tests for Covariance

Function	Purpose
pysht.covariance.wl_1samp, wl_2samp	Wu–Li random-projection tests
pysht.covariance.czz_identity_1samp	Chen–Zhang–Zhong identity test
pysht.covariance.czz_sphericity_1samp	Chen–Zhang–Zhong sphericity test
pysht.covariance.lc_2samp	Li–Chen dense covariance test
pysht.covariance.clx_2samp	Cai–Liu–Xia sparse maximum test
pysht.covariance.maximum_pairwise_bayes_factor_2samp	Lee–You–Lin known-zero-mean log Bayes factor
pysht.covariance.schott_2001_ksamp	Fixed-dimensional covariance homogeneity
pysht.covariance.schott_2007_ksamp	High-dimensional covariance homogeneity

[5] Simultaneous Tests for Mean and Variance

Function	Purpose
pysht.mean_variance.lrt_1samp	One normal mean and variance jointly
pysht.mean_variance.pn_2samp	Pearson–Neyman approximation
pysht.mean_variance.pl_2samp	Perng–Littell component combination
pysht.mean_variance.muirhead_2samp	Corrected likelihood-ratio approximation
pysht.mean_variance.exact_lrt_2samp	Exact Zhang–Xu–Chen calibration
pysht.mean_variance.lrt_2samp	Asymptotic two-sample LRT

[6] Simultaneous Tests for Mean and Covariance

Function	Purpose
pysht.mean_covariance.llzs_1samp	High-dimensional one-sample joint test
pysht.mean_covariance.lrt_1samp	Classical one-sample joint LRT
pysht.mean_covariance.hn_2samp	High-dimensional two-sample joint test

[7] Tests for Equality of Distributions

Function	Purpose
pysht.equaldist.bg_2samp	Biswas–Ghosh two-sample test
pysht.equaldist.energy_ksamp	DISCO/energy multi-sample test
pysht.equaldist.mmd_2samp	Characteristic-kernel MMD test

[8] Goodness-of-Fit: Normal Distribution

Function	Purpose
pysht.normality.shapiro_wilk, shapiro_francia	Shapiro normality tests
pysht.normality.jarque_bera, adjusted_jarque_bera, robust_jarque_bera	Moment normality tests
pysht.normality.henze_zirkler	Multivariate Henze–Zirkler test
pysht.normality.energy	Multivariate energy test

[9] Goodness-of-Fit: Uniform Distribution

Function	Purpose
pysht.uniformity.ym_interpoint	Yang–Modarres interpoint test
pysht.uniformity.ym_quantile	Yang–Modarres quantile test
pysht.uniformity.ehy	EHY nearest-neighbor rectangular-uniformity test

[10] Tests on Special Domains

Function	Purpose
pysht.simplex.uniformity	Dirichlet-alternative simplex-uniformity LRT
pysht.simplex.ehy_uniformity	Omnibus EHY simplex-uniformity test
pysht.simplex.alpha_energy_ksamp	Alpha-transformed compositional equality test

[11] Independence

Function	Purpose
pysht.independence.distance_covariance	Distance-covariance pairwise independence
pysht.independence.hsic	Kernel pairwise independence
pysht.independence.dhsic	Kernel joint independence of two or more blocks
pysht.independence.distance_multivariance	Distance-multivariance mutual independence

[12] Circular Data

Function	Purpose
pysht.circular.rayleigh	First-harmonic circular non-uniformity
pysht.circular.watson	Watson \(U^2\) omnibus circular uniformity
pysht.circular.hermans_rasson	Modified Hermans–Rasson omnibus test
pysht.circular.mardia_watson_wheeler_ksamp	Circular multi-sample equality

Correctness-gated research candidates

Ball Divergence, the Xue–Yao mean test, and the Yu–Li–Xue covariance combination have private research implementations but no public callable because their planned finite-resampling or joint-component calibration did not pass the release gate. The JWJWZ covariance and YLXL joint procedures remain formula-audit targets with no callable. A blocked method is never replaced by a silent fallback.

Result objects

Every public test returns an immutable StatisticalTestResult subtype. Frequentist tests report a statistic and p-value; resampling results add exactness and Monte Carlo diagnostics. The two maximum-pairwise-Bayes-factor functions instead report maximum and component log Bayes factors and have no p-value.

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