CAS Exam 8 Fall 2013, Question 2
Study guide: Exam 8
An actuary at a private passenger auto insurance company wishes to use a generalized linear model to create an auto frequency model using the data below.
Number of Claims
| Gender | Territory A | Territory B |
|---|---|---|
| Male | 700 | 600 |
| Female | 400 | 420 |
Number of Exposures
| Gender | Territory A | Territory B |
|---|---|---|
| Male | 1,400 | 1,000 |
| Female | 1,000 | 1,200 |
The model will include three parameters: \beta_1, \beta_2, and \beta_3, where \beta_1 is the average frequency for males, \beta_2 is the average frequency for Territory A, and \beta_3 is an intercept.
Part a (0.5 points)
Define the design matrix [X].
Part b (0.25 points)
Define the vector of responses [Y].
Part c (2.25 points)
Assuming \beta_3 = 0.35, solve a generalized linear model with a normal error structure and identity link function for \beta_1.
Part d (0.5 points)
The actuary determines that the analysis results would be improved by assuming a Poisson error structure with a log link function. Identify two reasons this structure may better suit this data.
Answer this question and see the worked solution