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Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 13J / d / Solution

A standard moment estimator is the Pearson dispersion estimator

ϕ = \frac{1}{n - p} i = 1 \sum n \frac{( Y _{i} - μ _{i} ) ^{2}}{V ( μ _{i} )} .

For Bernoulli data,

V (μ) = μ (1 - μ)

. The deviance divided by its residual degrees of freedom is a common alternative.

Solved by gpt-5.6-sol high.

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