Hii all Ch.7 : Risk models(1) On page22, the sums of compound Poisson distribution is given. The CDF and MGF of this are given as weighted average of CDF and MGFs of individual compound distributions. But what about the sum of compound Binomial and compound Negative binomial distributions? What is the reason behind that CDF and MGF are weighted average in case of compound Poisson dist. but not for Binomial and Neg. binomial? Please anyone explain. Thanks
Ohkay, getting now. But please help me with further two queries related to this: On page22 Here A is given as the sum of INDEPENDENT compound poisson random variables. And its MGF is the weighted average of individual MGFs. But if A would have the sum of INDEPENDENT AND IDENTICALLY distributed compound poisson random variables then the MGF(A) is just the [MGF(Si)]ⁿ i.e. Ma(t)= [Ms(t)]ⁿ , right? Also, In Q&A bank part-2, qus. 2.18(iv)- here Si are identically distributed compound negative binomial random variables , so we can easily find the MGF of T. But if Si would not have been identically distributed, then how can we find the MGF of T in this case? Thanks
1. correct 2. it would just be the product of the different compound distribution MGFs and would not be any recognisable distribution.
