TestStatistics: Available test statistics for symmetry tests

Description

The list of implemented test statistics and their functions

Usage

B1(X)
BH2(X)
BHC1(X, k)
BHC2(X, k)
BHI(X)
BHK(X)
CM(X)
FM(X)
HM(X, k)
K2U(X)
K2(X)
KS(X)
SGN(X)
WCX(X)
MGG(X)
MI(X)
MOI(X, k)
MOK(X, k)
NAC1(X, k)
NAC2(X, k)
NAI(X, k)
NAK(X, k)
RW(X)

Value

The value of the test statistic.

Arguments

X: the numeric vector for which to calculate the test statistic
k: the 'k' parameter in the formula (if applicable)

Test statistics

The list of available statitics in the format "code(s) : name (reference)"

MI : The Mira test statistic (see Msymmetry)
CM : The Cabilio–Masaro test statistic (see CMsymmetry)
MGG : The Miao, Gel and Gastwirth test statistic (see MGGsymmetry)
B1 : The \(\sqrt{b_1}\) test statistic (see UNKcentresymmetry)
KS : The Kolmogorov--Smirnov test statistic (see UNKcentresymmetry)
SGN : The Sign test statistic (see UNKcentresymmetry)
KS : The Wilcoxon test statistic (see UNKcentresymmetry)
FM : The characterization based test statistic (see CHsymmetry)
RW : The Rothman-Woodroofe test statistic (see RWsymmetry)
BHI : The Litvinova test statistic (see BHIsymmetry)
BHK : The Baringhaus and Henze supremum-type test statistic (see BHKsymmetry)
BH2 : The Baringhaus-Henze test statistic (see BHKsymmetry)
MOI and MOK : The Milošević and Obradović test statistics (see MOIMOKsymmetry)
NAI and NAK : The Nikitin and Ahsanullah test statistics (see NAINAKsymmetry)
K2 and K2U : The Božin, Milošević, Nikitin and Obradović Kolmogorov type statistics based on V- and U- statistics respectively (see K2K2Usymmetry)
NAC1, NAC2, BHC1 and BHC2 : The Allison and Pretorius test statistics (see Allisonsymmetry)

Details

Below is a list of the implemented test statistics in the package. Each statistic is listed by it's name, a code string (e.g. 'B1', CM','MOI') and the formula of the statistic which is evaluated. The code string is used as an argument to the symmetry_test function. Some statistics depend on a parameter 'k' which can be seen from the formulas and is also passed as an argument.