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#' @title Normal Joint Density
#' @description Returns a list with the product of the normal
#' densities and input data transformed by its distribution
#' function.
#' @param X A data frame with the predictor variables.
#' @param mu A vector with the estimates for \eqn{\mu}.
#' @param sd A vector with the estimates for \eqn{\sigma}.
join.normal <- function(X,mu,sd){
res <- t(apply(X, 1, function(x) dnorm(x,mu,sd,log = FALSE)))
U <- t(apply(X, 1, function(x) pnorm(x,mu,sd)))
res[res == 0] <- 1e-200
res <- apply(res, 1, function(x) sum(log(x)))
return(list(den = res, U = U))
}
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