#' @title generate samples from a Rayleigh distribution.
#' @description Implement a function to generate samples from a Rayleigh distribution.
#' @param x vector of quantiles
#' @param sigma a parameter
#' @param r number of sample
#' @param antithetic logical value, the default is true
#' @return a vector of size x\code{n}
#' @examples
#' \dontrun{
#' x <- seq(1, 10, 1)
#' sigma <- 2
#' r <- 10000
#' res <- MC.Phi(x, sigma, r)
#' }
#' @export
MC.Phi <- function(x, sigma, r, antithetic = TRUE)
{
y <- runif(r)
if(!antithetic) v <- runif(r)
else
v <- 1-y
y <- c(y, v)
cdf <- numeric(length(x))
for(i in 1:length(x))
{
g <- (y*x[i]^2)*exp(-(y*x[i]^2)/(2*(sigma^2)))
cdf[i] <- 1/(sigma^2)*mean(g)
}
cdf
}
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