the number of claims, n, and the total claim size y from the previous year, during which there were n = 10 claims with a total claim amount of y = 7.3
n = number of claims
y = total claim size
The number of claims in any given year follows a Poisson(λ) distribution with λ = 12
The individual claim sizes follow a Gamma(2, θ) distribution where θ is unknown.
Given θ, claim sizes are independent of each other.
- Identify a suitable prior π(θ) and briefly justify your choice
- Derive the posterior density π(θ|n, y).
- Now let n’ and z denote the number of claims and total claim amount respectively. Given n’ , derive the posterior predictive density π(z| n’, y). Hence find an expression for π(z|n, y) as an infinite sum.
