How do you choose values from a distribution according to their respective probabilities?

Question

John Bennett 2012-11-16

I wrote the following codes which represent a distribution:

 k=100;
 i=1:k;

%p distribution (ISD)

 p(i==1)=1/k;
 p(i~=1)=1./(i(i~=1).*(i(i~=1)-1));

%T distribution

 T(1<=i&i<=(k/R)-1)= R./(i(1<=i&i<=(k/R)-1).*k);
 T(i==round(k/R))=((R*log(R/delta))/k); 
 T(i>=(k/R)+1&i<=k)=0;

%beta is normalization factor. %It is calculated by adding both 1x100 arrays of p and T and summing each %array.

beta=sum(p+T);

%RSD

 M=(p+T)/beta; 
 stem(i,M);

Now, I want to choose i from M. How can I do this?

Any help would be much appreciated. Thanks

John Bennett 2012-11-16

Some additional information if you would want to run the code to see how the graph is like.

 c=0.1; k=100; delta=0.1; 
 R=c*log(k/delta)*sqrt(k);

Answer 1

Tom Lane 2012-11-16

Consider the randsample function if you have the Statistics Toolbox, or look here: