Thread: Mean and Variance of Mixed model

Hello, everyone;

I have a mixed probability function:
q+(1-q)*NB(0,r,p) for k=0;
(1-q)*NB(k,r,p) for k>0;

NB(k,r,p)=Gamma(k+r)/(Gamma(r)*(Gamma(k+1))*p^k*(1-p)^r

How can I calculate the Mean and Variance of this mixed function?

Thanks!
Maryann

Hello,

k takes integer values (as it looks like)

To get the expectation, first compute the integrals x*pdf for each k, then sum over k.
This will (I think) give the expectation you're looking for.

thanks!

Originally Posted by Moo

Hello,

k takes integer values (as it looks like)

To get the expectation, first compute the integrals x*pdf for each k, then sum over k.
This will (I think) give the expectation you're looking for.