1. The number of claims in a month for a portfolio of insurance policies is thought...

1. The number of claims in a month for a portfolio of insurance policies is thought to follow the Negative-binomial distribution with pdf

?(?) =( Γ(20+?) / Γ(? +1)Γ(20) ) . ?^20 . (1−?)^?, ? = 0,1,2,…

A sample of 4 months had claim numbers of 15, 25, 20 and 21.

a) There is no prior information for p. Using an uninformative prior to derive the posterior distribution for p. [12 marks]

b) Show that the mode of the Beta distribution with pdf ?(?) =( Γ(? +?) / Γ(?)Γ(?) ) . ?^(?−1) . (1−?)^(?−1), 0 < ? < 1

Expert Solution

orchestra answered 2 years ago

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