TestStatistics: Available test statistics for symmetry tests

In symmetry: Testing for Symmetry of Data and Model Residuals

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)

Arguments

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

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.

Each statistic is implemented as a function with the same name as the code string, so the name of the function is passed as the argument "stat" to the symmetry_test function

Value

The value of the test statistic.

Test statistics

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

• MI : The Mira test statistic (see \insertCiteMsymmetry)

• CM : The Cabilio–Masaro test statistic (see \insertCiteCMsymmetry)

• MGG : The Miao, Gel and Gastwirth test statistic (see \insertCiteMGGsymmetry)

• B1 : The \sqrt{b_1} test statistic (see \insertCiteUNKcentresymmetry)

• KS : The Kolmogorov–Smirnov test statistic (see \insertCiteUNKcentresymmetry)

• SGN : The Sign test statistic (see \insertCiteUNKcentresymmetry)

• KS : The Wilcoxon test statistic (see \insertCiteUNKcentresymmetry)

• FM : The characterization based test statistic (see \insertCiteCHsymmetry)

• RW : The Rothman-Woodroofe test statistic (see \insertCiteRWsymmetry)

• BHI : The Litvinova test statistic (see \insertCiteBHIsymmetry)

• BHK : The Baringhaus and Henze supremum-type test statistic (see \insertCiteBHKsymmetry)

• BH2 : The Baringhaus-Henze test statistic (see \insertCiteBHKsymmetry)

• MOI and MOK : The Milošević and Obradović test statistics (see \insertCiteMOIMOKsymmetry)

• NAI and NAK : The Nikitin and Ahsanullah test statistics (see \insertCiteNAINAKsymmetry)

• K2 and K2U : The Božin, Milošević, Nikitin and Obradović Kolmogorov type statistics based on V- and U- statistics respectively (see \insertCiteK2K2Usymmetry)

• NAC1, NAC2, BHC1 and BHC2 : The Allison and Pretorius test statistics (see \insertCiteAllisonsymmetry)

References

\insertAllCited

symmetry documentation built on March 31, 2023, 7:30 p.m.