Method names and acronyms#

pySHT uses short, lowercase author tokens for paper-specific Python functions: one author contributes a surname, while multiple authors contribute the initials of their surnames. Capitalization and full names remain visible in prose and printed results. Conventional statistical names remain conventional.

The qualified module is part of every public name. The covariance CLX test is public, while the distinct mean CLX and one-sample Fisher covariance identities are validation-blocked. The R names below are searchable migration metadata; pySHT does not expose them as callables.

Means and variances#

Token or name	Expanded method	Canonical Python function	SHT 0.1.9
Student t	Student one- and two-sample t tests	`mean.ttest_1samp`, `mean.ttest_2samp`	`mean1.ttest`, `mean2.ttest`
ANOVA	One-way analysis of variance	`mean.anova_oneway`	`meank.anova`
Hotelling	Hotelling’s \(T^2\) (1931)	`mean.hotelling_1samp`, `mean.hotelling_2samp`	`mean1.1931Hotelling`, `mean2.1931Hotelling`
Dempster	Dempster non-exact mean tests (1958)	`mean.dempster_1samp`, `mean.dempster_2samp`	`mean1.1958Dempster`, `mean2.1958Dempster`
BS	Bai–Saranadasa (1996)	`mean.bs_1samp`, `mean.bs_2samp`	`mean1.1996BS`, `mean2.1996BS`
SD	Srivastava–Du (2008)	`mean.sd_1samp`, `mean.sd_2samp`	`mean1.2008SD`, `mean2.2008SD`
Yao	Yao (1965)	`mean.yao_2samp`	`mean2.1965Yao`
Johansen	Johansen (1980)	`mean.johansen_2samp`	`mean2.1980Johansen`
NVM	Nel–Van der Merwe (1986)	`mean.nvm_2samp`	`mean2.1986NVM`
KY	Krishnamoorthy–Yu (2004)	`mean.ky_2samp`	`mean2.2004KY`
LJW	Lopes–Jacob–Wainwright (2011)	`mean.ljw_2samp`	`mean2.2011LJW`
CLX	Cai–Liu–Xia maximum mean test (2014)	— (validation-blocked; no public callable)	`mean2.2014CLX`
Thulin	Thulin random-subspace test (2014)	`mean.thulin_2samp`	`mean2.2014Thulin`
mxPBF / LYL	Lee–You–Lin maximum pairwise Bayes factor	`mean.maximum_pairwise_bayes_factor_2samp`	`mean2.mxPBF`
Schott	Schott k-sample mean test (2007)	`mean.schott_ksamp`	`meank.2007Schott`
ZX	Zhang–Xu (2009)	`mean.zx_ksamp`	`meank.2009ZX`
CPH	Cao–Park–He (2019)	`mean.cph_ksamp`	`meank.2019CPH`
chi-square	One-sample normal variance test	`variance.chisquare_1samp`	`var1.chisq`
F	Two-sample normal variance test	`variance.f_2samp`	`var2.F`
Bartlett	Bartlett homogeneity test (1937)	`variance.bartlett`	`vark.1937Bartlett`
Levene	Levene homogeneity test (1960)	`variance.levene`	`vark.1960Levene`
Brown–Forsythe	Brown–Forsythe homogeneity test (1974)	`variance.brown_forsythe`	`vark.1974BF`

Covariance and joint hypotheses#

Token or name	Expanded method	Canonical Python function	SHT 0.1.9
Fisher	Fisher covariance test (2012), withheld in 0.1.0	no public function	`cov1.2012Fisher`
WL	Wu–Li random-projection covariance tests (2015)	`covariance.wl_1samp`, `covariance.wl_2samp`	`cov1.2015WL`, `cov2.2015WL`
LC	Li–Chen covariance test (2012)	`covariance.lc_2samp`	`cov2.2012LC`
CLX	Cai–Liu–Xia covariance test (2013)	`covariance.clx_2samp`	`cov2.2013CLX`
mxPBF / LYL	Lee–You–Lin maximum pairwise Bayes factor	`covariance.maximum_pairwise_bayes_factor_2samp`	`cov2.mxPBF`
Schott 2001	Schott Wald covariance test	`covariance.schott_2001_ksamp`	`covk.2001Schott`
Schott 2007	Schott high-dimensional covariance test	`covariance.schott_2007_ksamp`	`covk.2007Schott`
LRT / AS	One-sample normal likelihood-ratio test; Arnold–Shavelle form (1998)	`mean_variance.lrt_1samp`	`mvar1.1998AS`, `mvar1.LRT`
PN	Pearson–Neyman (1930)	`mean_variance.pn_2samp`	`mvar2.1930PN`
PL	Perng–Littell (1976)	`mean_variance.pl_2samp`	`mvar2.1976PL`
Muirhead	Muirhead (1982)	`mean_variance.muirhead_2samp`	`mvar2.1982Muirhead`
exact LRT / ZXC	Zhang–Xu–Chen exact likelihood-ratio test (2012)	`mean_variance.exact_lrt_2samp`	`mvar2.2012ZXC`
LRT	Two-sample likelihood-ratio test	`mean_variance.lrt_2samp`	`mvar2.LRT`
LLZS	Liu–Liu–Zheng–Shi (2017)	`mean_covariance.llzs_1samp`	`sim1.2017Liu`
LRT	One-sample mean/covariance likelihood-ratio test	`mean_covariance.lrt_1samp`	`sim1.LRT`
HN	Hyodo–Nishiyama (2018)	`mean_covariance.hn_2samp`	`sim2.2018HN`

Distributional goodness-of-fit and special domains#

Token or name	Expanded method	Canonical Python function	SHT 0.1.9
BG	Biswas–Ghosh (2014)	`equaldist.bg_2samp`	`eqdist.2014BG`
Shapiro–Wilk	Shapiro–Wilk normality test (1965)	`normality.shapiro_wilk`	`norm.1965SW`
Shapiro–Francia	Shapiro–Francia normality test (1972)	`normality.shapiro_francia`	`norm.1972SF`
JB	Jarque–Bera normality test (1980)	`normality.jarque_bera`	`norm.1980JB`
AJB	Adjusted Jarque–Bera / Urzúa (1996)	`normality.adjusted_jarque_bera`	`norm.1996AJB`
RJB	Robust Jarque–Bera / Gel–Gastwirth (2008)	`normality.robust_jarque_bera`	`norm.2008RJB`
YM interpoint	Yang–Modarres interpoint test (2017)	`uniformity.ym_interpoint`	`unif.2017YMi`
YM quantile	Yang–Modarres quantile test (2017)	`uniformity.ym_quantile`	`unif.2017YMq`
simplex uniformity	Dirichlet likelihood-ratio test of uniformity	`simplex.uniformity`	`simplex.uniform`

pySHT-native research methods#

These names have no SHT crosswalk. Expanded surnames and common search terms are indexing metadata, not callable aliases.

Token or search name	Expanded method	Canonical Python function
CQ	Chen–Qin dense high-dimensional mean test (2010)	`mean.cq_2samp`
Li	Li fixed-small-sample, increasing-dimension Student tests (2023)	`mean.li_1samp`, `mean.li_2samp`, `mean.li_ksamp`
CZZ	Chen–Zhang–Zhong covariance identity and sphericity tests (2010)	`covariance.czz_identity_1samp`, `covariance.czz_sphericity_1samp`
DISCO / energy	Rizzo–Székely energy multi-sample equality test	`equaldist.energy_ksamp`
MMD	Maximum mean discrepancy	`equaldist.mmd_2samp`
Ball Divergence	Pan–Tian–Wang–Zhang distribution-equality test	— (validation-blocked; private research implementation)
distance covariance / dCov	Székely–Rizzo–Bakirov independence test	`independence.distance_covariance`
HSIC	Hilbert–Schmidt independence criterion	`independence.hsic`
dHSIC	Joint Hilbert–Schmidt independence criterion	`independence.dhsic`
distance multivariance	Böttcher–Keller-Ressel–Schilling mutual-independence test	`independence.distance_multivariance`
HZ	Henze–Zirkler multivariate-normality test	`normality.henze_zirkler`
energy normality	Székely–Rizzo multivariate-normality test	`normality.energy`
EHY	Ebner–Henze–Yukich nearest-neighbor uniformity statistic	`uniformity.ehy`, `simplex.ehy_uniformity`
alpha-energy	Sevinç–Tsagris compositional equality test	`simplex.alpha_energy_ksamp`
Rayleigh	First-harmonic circular-uniformity test	`circular.rayleigh`
Watson \(U^2\)	Omnibus circular-uniformity test	`circular.watson`
HR	Modified Hermans–Rasson Sobolev circular-uniformity test (1985)	`circular.hermans_rasson`
MWW	Mardia–Watson–Wheeler circular multi-sample test	`circular.mardia_watson_wheeler_ksamp`

The native-method catalog distinguishes public methods from research candidates that remain behind scientific gates.

Collision rule#

Years appear in a callable only when author token and sampling design collide inside one module. This is why the covariance module has schott_2001_ksamp and schott_2007_ksamp, while the mean module needs only schott_ksamp. If a future method still collides after adding its year, pySHT will append a descriptive statistic token rather than an arbitrary a or b.