从R翻译的随机生成代码在C ++中失败

Question

I am working on code implementing random generation algorithm for sampling from tails of normal distribution proposed by Christian Robert . The problem is that while code in R worked properly, then after translating it to C++ if fails. I can't see any reason for that and I'd be grateful for explaining me what went wrong and why.

Notice that the code below is far from elegant and efficient, it is simplified to make reproducible example.

Here is the function in R:

rtnormR <- function(mean = 0, sd = 1, lower = -Inf, upper = Inf) {
  lower <- (lower - mean) / sd 
  upper <- (upper - mean) / sd

  if (lower < upper && lower >= 0) {
    while (TRUE) {
      astar <- (lower + sqrt(lower^2 + 4)) / 2
      z <- rexp(1, astar) + lower
      u <- runif(1)
      if ((u <= exp(-(z - astar)^2 / 2)) && (z <= upper)) break
    }
  } else {
    z <- NaN
  }
  z*sd + mean
}

and here C++ version:

#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]

double rtnormCpp(double mean, double sd, double lower, double upper) {
  double z_lower = (lower - mean) / sd;
  double z_upper = (upper - mean) / sd;
  bool stop = false;
  double astar, z, u;

  if (z_lower < z_upper && z_lower >= 0) {
    while (!stop) {
      astar = (z_lower + std::sqrt(std::pow(z_lower, 2) + 4)) / 2;
      z = R::exp_rand() * astar + z_lower;
      u = R::unif_rand();
      if ((u <= std::exp(-std::pow(z-astar, 2) / 2)) && (z <= z_upper))
        stop = true;
    }
  } else {
    z = NAN;
  }
  return z*sd + mean;
}

Now compare the samples obtained using both functions (they are compared to dtnorm function from msm library):

xx = seq(-6, 6, by = 0.001)
hist(replicate(5000, rtnormR(mean = 0, sd = 1, lower = 3, upper = 5)), freq= FALSE, ylab = "", xlab = "", main = "rtnormR")
lines(xx, msm::dtnorm(xx, mean = 0, sd = 1, lower = 3, upper = 5), col = "red")
hist(replicate(5000, rtnormCpp(mean = 0, sd = 1, lower = 3, upper = 5)), freq= FALSE, ylab = "", xlab = "", main = "rtnormCpp")
lines(xx, msm::dtnorm(xx, mean = 0, sd = 1, lower = 3, upper = 5), col = "red")

As you can see, rtnormCpp returns biased samples. Do you have any ideas why?

Answer 1

While one can use either scale or rate in rexp() , the default parameterization is rate - so rexp(1,astar) has a mean of 1/astar , not astar .

If you change the relevant line of C++ code to

z = R::exp_rand() / astar + z_lower;

everything seems to work fine.