## [0] Utilities

usek1d()

Apply k-sample tests for two univariate samples

useknd()

Apply k-sample tests for two multivariate samples

## [1] Tests for Univariate Mean

mean1.ttest()

One-sample Student's t-test for Univariate Mean

mean2.ttest()

Two-sample Student's t-test for Univariate Means

meank.anova()

Analysis of Variance for Equality of Means

## [2] Tests for Multivariate Mean

mean1.1931Hotelling()

One-sample Hotelling's T-squared Test for Multivariate Mean

mean1.1958Dempster()

One-sample Test for Mean Vector by Dempster (1958, 1960)

mean1.1996BS()

One-sample Test for Mean Vector by Bai and Saranadasa (1996)

mean1.2008SD()

One-sample Test for Mean Vector by Srivastava and Du (2008)

mean2.1931Hotelling()

Two-sample Hotelling's T-squared Test for Multivariate Means

mean2.1958Dempster()

Two-sample Test for High-Dimensional Means by Dempster (1958, 1960)

mean2.1965Yao()

Two-sample Test for Multivariate Means by Yao (1965)

mean2.1980Johansen()

Two-sample Test for Multivariate Means by Johansen (1980)

mean2.1986NVM()

Two-sample Test for Multivariate Means by Nel and Van der Merwe (1986)

mean2.1996BS()

Two-sample Test for High-Dimensional Means by Bai and Saranadasa (1996)

mean2.2004KY()

Two-sample Test for Multivariate Means by Krishnamoorthy and Yu (2004)

mean2.2008SD()

Two-sample Test for High-Dimensional Means by Srivastava and Du (2008)

mean2.2011LJW()

Two-sample Test for Multivariate Means by Lopes, Jacob, and Wainwright (2011)

mean2.2014CLX()

Two-sample Test for High-Dimensional Means by Cai, Liu, and Xia (2014)

mean2.2014Thulin()

Two-sample Test for Multivariate Means by Thulin (2014)

mean2.mxPBF()

Two-sample Mean Test with Maximum Pairwise Bayes Factor

meank.2007Schott()

Test for Equality of Means by Schott (2007)

meank.2009ZX()

Test for Equality of Means by Zhang and Xu (2009)

meank.2019CPH()

Test for Equality of Means by Cao, Park, and He (2019)

## [3] Tests for Variance

var1.chisq()

One-Sample Chi-Square Test for Variance

var2.F()

Two-Sample F-Test for Variance

vark.1937Bartlett()

Bartlett's Test for Homogeneity of Variance

vark.1960Levene()

Levene's Test for Homogeneity of Variance

vark.1974BF()

Brown-Forsythe Test for Homogeneity of Variance

## [4] Tests for Covariance

cov1.2012Fisher()

One-sample Test for Covariance Matrix by Fisher (2012)

cov1.2015WL()

One-sample Test for Covariance Matrix by Wu and Li (2015)

cov2.2012LC()

Two-sample Test for High-Dimensional Covariances by Li and Chen (2012)

cov2.2013CLX()

Two-sample Test for Covariance Matrices by Cai, Liu, and Xia (2013)

cov2.2015WL()

Two-sample Test for Covariance Matrices by Wu and Li (2015)

covk.2001Schott()

Test for Homogeneity of Covariances by Schott (2001)

covk.2007Schott()

Test for Homogeneity of Covariances by Schott (2007)

## [5] Simultaneous Tests for Mean and Variance

mvar1.1998AS()

One-sample Simultaneous Test of Mean and Variance by Arnold and Shavelle (1998)

mvar1.LRT()

One-sample Simultaneous Likelihood Ratio Test of Mean and Variance

mvar2.1930PN()

Two-sample Simultaneous Test of Mean and Variance by Pearson and Neyman (1930)

mvar2.1976PL()

Two-sample Simultaneous Test of Mean and Variance by Perng and Littell (1976)

mvar2.1982Muirhead()

Two-sample Simultaneous Test of Mean and Variance by Muirhead Approximation (1982)

mvar2.2012ZXC()

Two-sample Simultaneous Test of Mean and Variance by Zhang, Xu, and Chen (2012)

mvar2.LRT()

Two-sample Simultaneous Likelihood Ratio Test of Mean and Variance

## [6] Simultaneous Tests for Mean and Covariance

sim1.2017Liu()

One-sample Simultaneous Test of Mean and Covariance by Liu et al. (2017)

sim1.LRT()

One-sample Simultaneous Likelihood Ratio Test of Mean and Covariance

sim2.2018HN()

Two-sample Simultaneous Test of Means and Covariances by Hyodo and Nishiyama (2018)

## [7] Tests for Equality of Distributions

eqdist.2014BG()

Test for Equality of Two Distributions by Biswas and Ghosh (2014)

## [8] Goodness-of-Fit : Normal Distribution

norm.1965SW()

Univariate Test of Normality by Shapiro and Wilk (1965)

norm.1972SF()

Univariate Test of Normality by Shapiro and Francia (1972)

norm.1980JB()

Univariate Test of Normality by Jarque and Bera (1980)

norm.1996AJB()

Adjusted Jarque-Bera Test of Univariate Normality by Urzua (1996)

norm.2008RJB()

Robust Jarque-Bera Test of Univariate Normality by Gel and Gastwirth (2008)

## [9] Goodness-of-Fit : Uniform Distribution

unif.2017YMi()

Multivariate Test of Uniformity based on Interpoint Distances by Yang and Modarres (2017)

unif.2017YMq()

Multivariate Test of Uniformity based on Normal Quantiles by Yang and Modarres (2017)

## [10] Tests on the Special Domains

### Probability Simplex

simplex.uniform()

Probability Simplex : Tests of Uniformity