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Re: st: random uniform variable with unequal probabilities


From   "Seed, Paul" <paul.seed@kcl.ac.uk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: random uniform variable with unequal probabilities
Date   Tue, 20 Nov 2012 10:25:16 +0000

On Mon, Nov 19, 2012 at 11:44 AM, Tomáš Houška <xbender@gmail.com> wrote:

> I need to generate a random variable from uniform distribution, but
> the probabilities are not not same for each option. The variable is
> discrete in interval [10,19] and is generated 10times. Each time one
> of the options has twice as high probability of occurring as the
> others. So in some sense, the draw is two-staged - in the first stage
> a random number (n) between 1 and 10 is generated and then that
> particular n-th option in the interval [10,19] has a probability 0.2
> of occurring, the other options have a probability 0.8/9 each.
>
> How can I generate such variable?

Actually, this _is_ a uniform distribution: It can be shown that 
Pr(X=x) = 0.1  for all integer x in the interval [10,19], = 0 otherwise.
So the double negative ("not not same") does for once equal a positive.

However,  the second sentence implies that what is produced is not a 
number, but a group of 10 numbers, and the 10^10 possible groups are 
definitely not all equally likely.  I expect that Nick's code can be 
easily adapted to give blocks of 10 numbers.

BW

Paul T Seed, Senior Lecturer in Medical Statistics, 
Division of Women's Health, King's College London
Women's Health Academic Centre, King's Health Partners 
(+44) (0) 20 7188 3642.



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