Java: random integer with non-uniform distribution

Question

How can I create a random integer n in Java, between 1 and k with a "linear descending distribution", i.e. 1 is

Answer 1

The simplest thing to do it to generate a list or array of all the possible values in their weights.

int k = /* possible values */
int[] results = new int[k*(k+1)/2];
for(int i=1,r=0;i<=k;i++)
   for(int j=0;j<=k-i;j++)
       results[r++] = i;
// k=4 => { 1,1,1,1,2,2,2,3,3,4 }

// to get a value with a given distribution.
int n = results[random.nextInt(results.length)];

This best works for relatively small k values.ie. k < 1000. ;)

For larger numbers you can use a bucket approach

int k = 
int[] buckets = new int[k+1];
for(int i=1;i

The cost of the binary search is fairly small but not as efficient as a direct look up (for a small array)

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For an arbitary distrubution you can use a double[] for the cumlative distrubution and use a binary search to find the value.