Simulating of Beta-Binomial distribution

[Yuliya]

Hi,

I would highly appreciate it if you could give me any guidance how I can simulate the joint Beta-binomial distribution.

Thank you in advance.

Regards,

Yuliya

[RahulG]

See if this pdf help you

https://www.sas.com/storefront/aux/en/spsimulationofdata/65378_excerpt.pdf

[Yuliya]

Hi,

thank you very much. Unfortunately, there is only ine part of the book with the simplest simulations. I need to simulate a joint distribution Beta - binomial. Any ideas?

Thank you again.

Regards,

Yuliya

[Rick_SAS]

I think @RahulG's intent was to point you to the book Simulating Data with SAS, rather than suggest that your answer was found in the free chapter.

If you read and understand the blog the @Ksharp linked to, you should have no problem modifying it to the beta-binomial.  Start there, and post again if you have a particular question.

[Ksharp]

You should post it at IML forum.
Here is Gamma+Possion distribution:

http://blogs.sas.com/content/iml/2014/04/02/interpret-nb-distribution.html

[Yuliya]

Thank you very much!

[Ksharp]

OK. Here is Beta-Binomial distribution.
Beta-Binomial is usually for Overdispersion Models .






data have;
pi=0.3;
Rho=0.2;
m=30;

c=(1-Rho**2)/(Rho**2) ;
a=c*pi;
b=c*(1-pi);

call streaminit(1234);
do i=1 to 1000000;
 p=rand('beta',a,b);
 x=rand('binomial',p,m);
 output;
end;
keep x;
run;


proc sgplot data=have;
 vbar x / stat=percent;
run;

[Yuliya · Accepted solution]

Hi everyone,

thank you very much for your help.

I simulated with both ways.

Have a nice weekend.

Regards,

Yuliya

[Abdelkarim]

Hello Ksharp;

I could not find PDF, CDF, and inverse CDF call functions for beta binomial in SAS. I appreciate your help in determining all possible values of unknown parameters, say eta1 and eta2 (reparameterized parameters) that satisfies two inverse beta binomial functions simultaneously. For example, if the inverse CDF of beta binomial is Q, then how we can solve the following equations together for eta1 and eta2 :

6=Q(0.8, eta1,eta2) and 2=Q(0.1,eta1,eta2)  and once we have these values, how we can keep them to be used in a following step in the program.                       

Thank you

[Ksharp]

Sorry. It is out of my knowledge. But maybe @Rick_SAS could help you.
Post your question at IML forum. Since it is about data simulation.

[Rick_SAS]

This thread is old and SOLVED (closed). It contains a link to a blog post that describes how to simulate from a compound distribution. The beta-binomial distribution is compound, so to generate random draws from the beta-binomial you can first draw p from a beta distribution and then draw X from the binomial(p) distribution.

If you want to use the other probability function such as PDF, CDF, and QUANTILE, please start a new thread in in this forum or in the Base SAS Community.

[Abdelkarim]

Hi,

How can I start a new thread in in this forum?

Thank you 

[Rick_SAS]

Click the "Please ask a new question" link at the top right. You can also go up one level to the General SAS Programming Community. However, if it is a question about the beta-binomial distribution you might want to post to the SAS Statistical Community

[mikami-ms]

I'm not sure, but if c=a+b and rho=1/(a+b+1), c=(1-rho)/rho?

[Rick_SAS]

See the article "Simulate data from the beta-binomial distribution in SAS."

If you also need the PDF, CDF, and quantile functions, see the article "Compute the CDF and quantiles of discrete distributions."