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st: R: How to sample from a Multinomial distribution


From   "Carlo Lazzaro" <carlo.lazzaro@tin.it>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: R: How to sample from a Multinomial distribution
Date   Thu, 28 Feb 2008 09:09:31 +0100

Dear Tiago,

Provided that I have understood your question well, I suppose you have to
draw random samples from a so called Dirichlet distribution (please, see
Briggs A, Schulper M, Claxton K. Decision Modelling for Health Economic
Evaluation. Oxford: Oxford University Press, 2006: 116-118).

Assuming you start with counts instead of probabilities, I would suggest you
to fit three independent gamma distributions (where parameter alfa is the
mean^2/SE^2 and parameter beta is SE^2/mean of your original dataset)and use
the inverse gamma for random sampling and eventually obtain the
probabilities you are seeking.


Translating into Stata, it would be like this (please, see the example
below).
------------------------------begin example-------------------------- cap
program drop simgamma

program simgamma, rclass
 
args a1 b1 a2 b2 a3 b3 
  
tempname beta1 beta2 beta3    
   
scalar `beta1' = `b1'*invgammap(`a1',uniform())
 
scalar `beta2' = `b2'*invgammap(`a2',uniform())

scalar `beta3' = `b3'*invgammap(`a3',uniform())
 
return scalar beta1 = `beta1'
 
return scalar beta2 = `beta2'

return scalar beta3 = `beta3'

  
end

clear

set obs 10000

g a1=1

g b1=1251

g a2=1

g b2=350

g a3=1

g b3=116

simulate beta1=r(beta1) beta2=r(beta2) beta3=r(beta3), reps(10000) nodots:
simgamma a1 b1 a2 b2 a3 b3 

egen first_tot=  rowtotal ( beta1 beta2 beta3)

g pG1= beta1/ first_tot

g pG2= beta2/ first_tot

g pG3= beta3/ first_tot
----------------end example-------------------------------------------------

Please consider that values for a(lfa) and b(eta) in my example should be
changed according to your original data.

HTH and Kind Regards,

Carlo
-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di
tiago.pereira@incor.usp.br
Inviato: mercoledý 27 febbraio 2008 19.42
A: statalist@hsphsun2.harvard.edu
Oggetto: st: How to sample from a Multinomial distribution

Dear Statalisters,

I have to generate data for a sample, which has three groups (G1, G2 and
G3). In this respect,  the probability distribution for the G1, G2 and G3
follows a multinomial distribution with parameter vector P = (pG1 ,pG2
,pG3 ).

I have used -genbinomial- to generate the first two groups, and then the
last one is calculate by subtraction. Since this is not an elegant way to do
that, is the any routine that does in Stata the task above mentioned ?
I have not found anything yet.

Thanks in advance!

Tiago


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