Random Number Generator, lower numbers have higher chance

Hi. I am trying to create a script for generating a random number, with lower numbers having a higher chance of being picked.

This will be in the range of 1 to 20

The percent chance is going to be based on (0.5)^n

So the chance of getting a 1 is 50%, the chance of getting a 2 is 25%, 3 is 12.5% and so on....

I am having trouble getting started with this. I'm not even sure if there is a way. You don't have to write this out, I would just like someone to help me get started or send me in the right direction.

Answer 1

[Walter Roberson]

min(ceil(-log2(rand)),20)

[owr]

Thats very nice Walter!

[Nick]

Thanks for this! after looking at it really closely I understand it!

Answer 2

[owr]

If you have a recent version of MATLAB (2012A) and the Statistics Toolbox check out the function "datasample" with the optional parameter 'Weights'.

If not, try using "rand" which generates random numbers uniformly on interval [0,1]. If number is between 0 and 0.5, call it a "1", between 0.5 and 0.75, call it a "2", etc. "histc" should help with this by setting your "edges" to the cumulative sum of your probabilities, ie, 0.5, 0.75, 0.875,...

Thats hwo I would proceed. There might be something pre-built on the file Exchange that does this, or a MATLAB function Im missing.

Good luck.

Answer 3

[Stephen]

just create the distribution

    n=1:20;
    dist = [];  
  for t=1:20
    dist = [dist, n(t) * ones(1, round( 20/n(t) ))];
  end

then dist(randi(numel(dist))) would give you your weighted answer

you can check hist(dist(randi(numel(dist,1e5,1))),100) to see that the probability is close enough