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# quantile function of the truncated gamma with shape=1/2,
# scale=8*lambda2/lambda1^2, and domain=(1,infinity)
qtau <- function(p, lambda1, lambda2, log.p=FALSE) {
scale <- 8*lambda2/lambda1^2
if(log.p) {
aux <- pnorm(-sqrt(2/scale), log.p=log.p)
tau <- 0.5*scale*qnorm(exp(aux) - exp(aux + p))^2
} else {
tau <- 0.5*scale*qnorm((1 - p)*pnorm(-sqrt(2/scale)))^2
}
return(tau)
}
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