Random Distribution – How to Generate Random Numbers with a Negative Sloping Distribution?

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Given a maximum integer value M, I want to generate N integer values that are distributed with a lower frequency when approaching M (preferably M should still have a non-zero probability).
I don't really care much about the probability function, let's assume (half of) a normal distribution.

How would I do that if I don't want to keep a history?

for i := 1 to N do GetNextTestValue(M)

What could GetNextTestValue look like?
FWIW I'm doing this in Delphi

Best Answer

Building off of GrandmasterB's comment about pick two and select the lowest, I wrote a quick perl script to plot the random numbers and see the distributions - Pick the lowest of two provides one distribution, but others provide other distributions...

First, the code to see how it works and reproduce the results if you so desire.

#!/usr/bin/perl

use strict;
my $count = shift @ARGV;
my $nth = shift @ARGV;

my @nums = ();

for(my $i = 0; $i < 10_000; $i++) {
    my @rnd;
    for(my $j = 0; $j < $count; $j++) {
        push @rnd, int(rand(100));
    }
    @rnd = sort { $a <=> $b } @rnd;
    $nums[$rnd[$nth]]++;
}

for(my $i = 0; $i < 100; $i++) {
    print "$i\t" . (defined $nums[$i] ? $nums[$i] : 0) . "\n";
}

The pick min(rand(100),rand(100)) produces a straight line distribution sloping down.

If you min(rand(100),rand(100), rand(100)), you can see a bit of a curve to it.

Exploring this just a bit further... Picking the middle number of 7 produces something that looks more like a nice bell curve.

While the 2nd number of 7 produces a skewed one.

So, from this and the application of some stats to decide what shape you want it (or throwing out samples that don't meet the desired range to get the desired shape and skew)

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