Sampling from a mixture of distributions (II)

The complete algorithm for sampling from a mixture distribution is:

Choose a component.
Generate a normal random number using the mean and standard deviation of the selected component.

choose_component(), from the last exercise, is provided. Here you'll complete the second step and complete the definition of rmix().

This exercise is part of the course

Optimizing R Code with Rcpp

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Exercise instructions

Check that there are as many standard deviations as weights. That is, the size of sds is the same as d.
Calculate total_weight as the sum of the weights.
Choose a component by calling choose_component().
Simulate from the chosen component by generating a normal random number with the jth element of means and sds.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

#include 
using namespace Rcpp;

// From previous exercise; do not modify
// [[Rcpp::export]]
int choose_component(NumericVector weights, double total_weight) {
  double x = R::runif(0, total_weight);
  int j = 0;
  while(x >= weights[j]) {
    x -= weights[j];
    j++;
  }
  return j;
}

// [[Rcpp::export]]
NumericVector rmix(int n, NumericVector weights, NumericVector means, NumericVector sds) {
  // Check that weights and means have the same size
  int d = weights.size();
  if(means.size() != d) {
    stop("means size != weights size");
  }
  // Do the same for the weights and std devs
  if(___) {
    stop("sds size != weights size");
  }
  
  // Calculate the total weight
  double total_weight = ___;
  
  // Create the output vector
  NumericVector res(n);
  
  // Fill the vector
  for(int i = 0; i < n; i++) {
    // Choose a component
    int j = ___(___, ___);
    
    // Simulate from the chosen component
    res[i] = ___::___(___, ___);
  }
  
  return res;
}

/*** R
  weights <- c(0.3, 0.7)
  means <- c(2, 4)
  sds <- c(2, 4)
  rmix(10, weights, means, sds)
*/

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