Nothing
liu <- function(q, lambda, h = rep(1, length(lambda)), delta = rep(0, length(lambda))) {
r <- length(lambda)
if (any(delta < 0)) stop("All non centrality parameters in 'delta' should be positive!")
if (length(h) != r) stop("lambda and h should have the same length!")
if (length(delta) != r) stop("lambda and delta should have the same length!")
c1 <- sum(lambda * h) + sum(lambda * delta)
c2 <- sum(lambda ^ 2 * h) + 2 * sum(lambda ^ 2 * delta)
c3 <- sum(lambda ^ 3 * h) + 3 * sum(lambda ^ 3 * delta)
c4 <- sum(lambda ^ 4 * h) + 4 * sum(lambda ^ 4 * delta)
s1 <- c3 / (c2 ^ (3 / 2))
s2 <- c4 / c2 ^ 2
muQ <- c1
sigmaQ <- sqrt(2 * c2)
tstar <- (q - muQ) / sigmaQ
if (s1 ^ 2 > s2) {
a <- 1 / (s1 - sqrt(s1 ^ 2 - s2))
delta <- s1 * a ^ 3 - a ^ 2
l <- a ^ 2 - 2 * delta
} else {
a <- 1 / s1
delta <- 0
l <- c2 ^ 3 / c3 ^ 2
}
muX <- l + delta
sigmaX <- sqrt(2) * a
Qq <- pchisq(tstar * sigmaX + muX, df = l, ncp = delta, lower.tail = FALSE)
return(Qq)
}
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