IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit
A Poisson distribution is fitted to claim counts per policy by estimating the mean from the data. After grouping the counts into the categories 0, 1, 2, 3 and 4 or more, a chi-square goodness of fit test is performed. How many degrees of freedom should be used?
Degrees of freedom are 3. With five categories the base is 5 - 1 = 4, and one further degree is lost because the Poisson mean was estimated from the same data.
- A5
- B4
- C3Correct
- D2
- 1
Explanation
There are 5 categories, so degrees of freedom start at 5 - 1 = 4. One parameter (the Poisson mean) is estimated from the data, so subtract 1 more, giving 3. Using 4 ignores the estimated parameter.
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