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Math Help - Mean and Variance of Mixed model

  1. #1
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    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
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  2. #2
    Moo
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    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.
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  3. #3
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    thanks!


    Quote Originally Posted by Moo View Post
    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.
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