The data below, taken from Greenwood and Yule, (1920)3 , shows the frequency of accidents occurring, over a ?ve-week period, to 647 women making high explosives during World War I.
|
Number of Accidents
|
Observed Frequency
|
|
0
|
447
|
|
1
|
132
|
|
2
|
42
|
|
3
|
21
|
|
4
|
3
|
|
5+
|
2
|
(i) If X is the random variable representing the number of accidents, determine the mean and the variance of this clearly Poisson-like random variable, and con?rm that this is an over-dispersed Poisson variable for which the Poisson population parameter, rather than being constant, varies across the population.
(ii) For over-dispersed Poisson variables such as this, the more appropriate model is the negative binomialNBi(α, p). Determine the method of moments estimates for the unknown parameters α and p for this data set.