Let the number X of accidents have a Poisson distribution with mean . Suppose , the liability

Let the number X of accidents have a Poisson distribution with mean λθ. Suppose λ, the liability to have an accident, has, given θ, a gamma pdf with parameters α = h and β = h⁻¹; and θ, an accident proneness factor, has a generalized Pareto pdf with parameters α, λ = h, and k. Show that the unconditional pdf of X is

sometimes called the generalized Waring pmf.

Transcribed Image Text:

I(a + k)I(a+h)T(a+h+k)T(h+k)T(k+x) T(a)(a +k+h)T(h)T(k)[(a+h+k+x)x! ' x = 0, 1, 2,...,