Nothing
halfnorm.randomnr.ci <- function(stat, se, alpha = 0.05, type = "dist") {
z <- stat/se
k <- length(stat)
za <- qnorm(1 - alpha)
Nr <- sum( z )^2 / za - k
za4 <- za^4
f <- (k - 1) / k
lam <- k
if ( type == "dist" ) {
m1 <- sqrt(2 / pi) ; s1 <- 1 - 2/pi
a1 <- ( ( 4 * lam^3 + 6 * lam^2 + lam ) * m1^4 + (4 * lam^3 + 16 * lam^2 + 6 * lam) * m1^2 * s1 ) / za4
a2 <- ( 2 * lam^2 + 3 * lam ) * s1^4 / za4 - 2 * ( ( 2 * lam^2 + lam ) * m1^2 + lam * s1 )/ za^2 + lam
variance <- a1 + a2
ci <- c( Nr - qnorm(1 - alpha/2) * sqrt(variance), Nr + qnorm(1 - alpha/2) * sqrt(variance) )
} else if ( type == "mom" ) {
m2 <- mean(z) ; s2 <- f * var(z)
a1 <- ( ( 4 * lam^3 + 6 * lam^2 + lam ) * m2^4 + (4 * lam^3 + 16 * lam^2 + 6 * lam) * m2^2 * s2 ) / za4
a2 <- ( 2 * lam^2 + 3 * lam ) * s2^4 / za4 - 2 * ( ( 2 * lam^2 + lam ) * m2^2 + lam * s2 )/ za^2 + lam
variance <- a1 + a2
ci <- c( Nr - qnorm(1 - alpha/2) * sqrt(variance), Nr + qnorm(1 - alpha/2) * sqrt(variance) )
} else if ( type == "both" ) {
m1 <- sqrt(2 / pi) ; s1 <- 1 - 2/pi
a1 <- ( ( 4 * lam^3 + 6 * lam^2 + lam ) * m1^4 + (4 * lam^3 + 16 * lam^2 + 6 * lam) * m1^2 * s1 ) / za4
a2 <- ( 2 * lam^2 + 3 * lam ) * s1^4 / za4 - 2 * ( ( 2 * lam^2 + lam ) * m1^2 + lam * s1 )/ za^2 + lam
vardist <- a1 + a2
cidist <- c( Nr - qnorm(1 - alpha/2) * sqrt(vardist), Nr + qnorm(1 - alpha/2) * sqrt(vardist) )
m2 <- mean(z) ; s2 <- f * var(z)
a1 <- ( ( 4 * lam^3 + 6 * lam^2 + lam ) * m2^4 + (4 * lam^3 + 16 * lam^2 + 6 * lam) * m2^2 * s2 ) / za4
a2 <- ( 2 * lam^2 + 3 * lam ) * s2^4 / za4 - 2 * ( ( 2 * lam^2 + lam ) * m2^2 + lam * s2 )/ za^2 + lam
varmom <- a1 + a2
cimom <- c( Nr - qnorm(1 - alpha/2) * sqrt(varmom), Nr + qnorm(1 - alpha/2) * sqrt(varmom) )
variance <- c(vardist, varmom)
names(variance) <- c( "distributional variace", "moments variance" )
ci <- rbind(cidist, cimom)
rownames(ci) <- c( "distribution based", "moments based")
}
list(Nr = Nr, variance = variance, ci = ci )
}
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