> To favor the popular, you choose a random number N from 0 to 549, then traverse the set of animals, subtracting each one's popularity from N until N goes negative, and that's the animal you choose.

I don't think that's a good idea. More than 80% of your random numbers will be bigger than 100, which means none will be picked.

This also explains why you have problems inverting this "solution".

Furthermore a linear search in the hash won't be truly random, because the hash order is fixed within the duration of a run. This will result in a disproportionate representation of the early entries.

Solution is easy:

sort the N entries and chose a modified random function which favors one end of the range, like $i = int $N * rand() ** $e and $j = $N - 1 - $i for index in your sorted list. The way you chose $e > 1 will decide about the degree of bias ( $e=1 means no bias)

Just test the distribution of the indices:

  DB<41> %h=();$e=3; $N=10; $h{ int $N * rand() **$e }++ for 1..10000

  DB<42> x \%h
0  HASH(0x2f25fe8)
   0 => 4670
   1 => 1215
   2 => 838
   3 => 686
   4 => 550
   5 => 484
   6 => 407
   7 => 388
   8 => 426
   9 => 336
  DB<43>

[download]

In this example the first 10% are more than 10 times more likely to be picked than the last 10%.

Of course YMMV about the distribution you prefer, but the basic idea is the same.

Cheers Rolf
(addicted to the Perl Programming Language :)
Wikisyntax for the Monastery

In reply to Re: Randomly choosing from a set of alternatives with varying popularity by LanX
in thread Randomly choosing from a set of alternatives with varying popularity by ibm1620

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