R/AAA_statistics_docs.R

In symmetry: Testing for Symmetry of Data and Model Residuals

#' Available test statistics for symmetry tests
#'
#' The list of implemented test statistics and their functions
#'
#' 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 \link{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
#' \link{symmetry_test} function
#'
#' @section Test statistics:
#' The list of available statitics in the format "code(s) : name (reference)"
#'
#' * MI : The Mira test statistic (see \insertCite{M}{symmetry})
#' * CM : The Cabilio–Masaro test statistic (see \insertCite{CM}{symmetry})
#' * MGG : The Miao, Gel and Gastwirth test statistic (see \insertCite{MGG}{symmetry})
#' * B1 : The \eqn{\sqrt{b_1}} test statistic (see \insertCite{UNKcentre}{symmetry})
#' * KS : The Kolmogorov--Smirnov test statistic (see \insertCite{UNKcentre}{symmetry})
#' * SGN : The Sign test statistic (see \insertCite{UNKcentre}{symmetry})
#' * KS : The Wilcoxon test statistic (see \insertCite{UNKcentre}{symmetry})
#' * FM : The characterization based test statistic (see \insertCite{CH}{symmetry})
#' * RW : The Rothman-Woodroofe test statistic (see \insertCite{RW}{symmetry})
#' * BHI : The Litvinova test statistic (see \insertCite{BHI}{symmetry})
#' * BHK : The Baringhaus and Henze supremum-type test statistic (see \insertCite{BHK}{symmetry})
#' * BH2 : The Baringhaus-Henze test statistic (see \insertCite{BHK}{symmetry})
#' * MOI and MOK : The Milošević and Obradović test statistics (see \insertCite{MOIMOK}{symmetry})
#' * NAI and NAK : The Nikitin and Ahsanullah test statistics (see \insertCite{NAINAK}{symmetry})
#' * K2 and K2U : The Božin, Milošević, Nikitin and Obradović Kolmogorov type statistics based on V- and U- statistics respectively (see \insertCite{K2K2U}{symmetry})
#' * NAC1, NAC2, BHC1 and BHC2 : The Allison and Pretorius test statistics (see \insertCite{Allison}{symmetry})
#' @param X the numeric vector for which to calculate the test statistic
#' @param k the 'k' parameter in the formula (if applicable)
#' @return The value of the test statistic.
#' @references \insertAllCited{}
#' @aliases TestStatistics
#' @name TestStatistics
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