43 lines
1.2 KiB
R
43 lines
1.2 KiB
R
# Approximate Epps-Pulley normality test
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#
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# Author: Francois Pelletier
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#
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# LGPL 3.0
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###############################################################################
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#' Approximate Epps-Pulley normality test
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#'
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#' An Approximation to the Limit Distribution
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#' of the Epps-Pulley Test Statistic for Normality
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#' By N. Henze
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#' Metrika (1990) 37:7-18
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#' @param x Sample
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#' @param alpha Tolerance level
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#' @return A list containing the test statistics
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#' @export EppsPulley.test
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#' @author François Pelletier
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EppsPulley.test <- function(x,alpha=0.05)
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{
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## Statistics
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n <- length(x)
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if (n<10) stop("n must be > 10")
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xbar <- mean(x)
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S <- sd(x)
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## Constants
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gamma <- 3.55295
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delta <- 1.23062
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lambda <- 2.26664
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xi <- -0.020682
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## Calculations
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T <- 2/n*sum(outer(x,x,function(x,y) exp(-0.5*(x-y)^2 / S^2))*
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outer(1:n,1:n,function(x,y) x<y)) -
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sqrt(2)*sum(exp(-0.25*(x-xbar)^2/S^2))+
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n/sqrt(3)+1
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Tmod <- (T - 0.365/n + 1.34/n^2)*(1 + 1.3/n)
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Z <- gamma+delta*log((Tmod-xi)/(xi+lambda-Tmod))
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Pvalue <- 1-pnorm(Z)
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reject <- Pvalue<alpha
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cat(sprintf("\nEpps-Pulley Normality test\n\n T: %f\n T*: %f\np-value: %f\n\n",T,Tmod,Pvalue))
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list(Tstat=T,Tmod=Tmod,Zscore=Z,Pvalue=Pvalue,Reject=reject)
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}
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