Anscombe-Glynn, Bonett-Seier, D'Agostino

Fri, Apr 29, 2005 11:11 AM

Dear useRs,

I was searching CRAN for implementation of kurtosis and skewness tests, 
and found that there is some kind of lack on it.

So, I have written three functions:

1. Anscombe-Glynn test for kurtosis
2. Bonett-Seier test based on Geary's kurtosis (which is not widely 
known, but I was inspired by original paper describing it, found 
coincidentally in Elsevier database)
3. D'Agostino test for skewness

These three functions are not enough to make another small package, so I 
am waiting for ideas about implementing it in some existing package. If 
there is a need, I will contact maintainer and write manpages with 
appropriate examples and references.

Regards,

Lukasz Komsta
Department of Medicinal Chemistry
Medical University of Lublin
6 Chodzki, 20-093 Lublin, Poland
Fax +48 81 7425165


Code:

agostino.test <- function (x, alternative=c("two.sided","less","greater"))
{
     DNAME <- deparse(substitute(x))
     x <- sort(x[complete.cases(x)])
     n <- length(x)

	s <- match.arg(alternative)
	alter <- switch(s, two.sided=0, less=1, greater=2)

     if ((n < 8 || n > 46340))
         stop("sample size must be between 8 and 46340")

	s3 <- (sum((x-mean(x))^3)/n)/(sum((x-mean(x))^2)/n)^(3/2)
	y <- s3*sqrt((n+1)*(n+3)/(6*(n-2)))
	b2 <- 3*(n*n+27*n-70)*(n+1)*(n+3)/((n-2)*(n+5)*(n+7)*(n+9))
	w <- sqrt(-1+sqrt(2*(b2-1)));
	d <- 1/sqrt(log10(w));
	a <- sqrt(2/(w*w-1));
	z <- d*log10(y/a+sqrt((y/a)^2+1));

     pval <- pnorm(z, lower.tail = FALSE)

if (alter == 0) {
	pval <- 2*pval
	if (pval > 1) pval<-2-pval
	alt <- "data have a skewness"
	}
else if (alter == 1)
	{
	alt <- "data have positive skewness"
	}
else
	{
	pval <- 1-pval
	alt <- "data have negative skewness"
	}


     RVAL <- list(statistic = c(g1 = s3, z = z), p.value = pval, 
alternative = alt, method = "D'Agostino skewness test",
         data.name = DNAME)
     class(RVAL) <- "htest"
     return(RVAL)
}



bonett.test <- function (x, alternative=c("two.sided","less","greater"))
{
     DNAME <- deparse(substitute(x))
     x <- sort(x[complete.cases(x)])
     n <- length(x)

	s <- match.arg(alternative)
	alter <- switch(s, two.sided=0, less=1, greater=2)

	rho <- sqrt(sum((x-mean(x))^2)/n);
	tau <- sum(abs(x-mean(x)))/n;
	omega <- 13.29*(log(rho)-log(tau));
	z <- sqrt(n+2)*(omega-3)/3.54;

     pval <- pnorm(z, lower.tail = FALSE)

if (alter == 0) {
	pval <- 2*pval
	if (pval > 1) pval<-2-pval
	alt <- "kurtosis is not equal to 3"
	}
else if (alter == 1)
	{
	alt <- "kurtosis is greater than 3"
	}
else
	{
	pval <- 1-pval
	alt <- "kurtosis is lower than 3"
	}


     RVAL <- list(statistic = c(tau = tau, z = z), alternative = alt, 
p.value = pval, method = "Bonett-Seier kurtosis test",
         data.name = DNAME)
     class(RVAL) <- "htest"
     return(RVAL)
}



anscombe.test <- function (x, alternative=c("two.sided","less","greater"))
{
     DNAME <- deparse(substitute(x))
     x <- sort(x[complete.cases(x)])
     n <- length(x)
	s <- match.arg(alternative)
	alter <- switch(s, two.sided=0, less=1, greater=2)

	b <- n*sum( (x-mean(x))^4 )/(sum( (x-mean(x))^2 )^2);

	eb2 <- 3*(n-1)/(n+1);
	vb2 <- 24*n*(n-2)*(n-3)/ ((n+1)^2*(n+3)*(n+5));
	m3 <- (6*(n^2-5*n+2)/((n+7)*(n+9)))*sqrt((6*(n+3)*(n+5))/(n*(n-2)*(n-3)));
	a <- 6+(8/m3)*(2/m3+sqrt(1+4/m3));
	xx <- (b-eb2)/sqrt(vb2);
	z <- ( 1-2/(9*a)-( (1-2/a) / (1+xx*sqrt(2/(a-4))) )^(1/3))/ sqrt(2/(9*a));

     pval <- pnorm(z, lower.tail = FALSE)

if (alter == 0) {
	pval <- 2*pval
	if (pval > 1) pval<-2-pval
	alt <- "kurtosis is not equal to 3"
	}
else if (alter == 1)
	{
	alt <- "kurtosis is greater than 3"
	}
else
	{
	pval <- 1-pval
	alt <- "kurtosis is lower than 3"
	}

     RVAL <- list(statistic = c(b2 = b, z = z), p.value = pval, 
alternative = alt, method = "Anscombe-Glynn kurtosis test",
         data.name = DNAME)
     class(RVAL) <- "htest"
     return(RVAL)
}