Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 36 / 2 / e

Table of contents
- Solution e

Solution

For a shape-rate gamma distribution

Gamma (a, b)

, the mean and variance conditions require

\frac{a}{b} = 1, \frac{a}{b ^{2}} = 0.2 5^{2} = \frac{1}{16} .

The first equation gives

a = b

, and the second then gives

a = b = 16

. Hence

λ_{i} \sim Gamma (16, 16) .

This proper prior distribution is centered on the national reference risk, while allowing genuine between-area variation.

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