SOA Exam ASTAM Sample Question 18

Study guide: Exam ASTAM

A claims study examines the frequency of automobile claims among 400 policies. An actuarial assistant has fit several frequency models (including Zero-Modified distributions) to the claims data using Maximum Likelihood Estimation. Summarized results are shown below.

	Poisson	ZM Poisson	Geometric	ZM Geometric	Neg Binomial	ZM Neg Binomial
Parameters	1	2	1	2	2	3
$p_0$		0.5625		0.5625		0.5625
$\lambda$	0.6175	0.7339
$r$					2.1894	0.4963
$\beta$			0.6175	0.4114	0.2853	0.5715
Log-Likelihood function	-427.8	-426.2	-430.2	-423.2	-424.5	-423.1
SBC Statistic	-430.8	-432.2	-433.2	-429.2	-430.5	-432.0
$\chi^2$ Statistic	6.07	3.29	14.53	1.26	5.15	1.14
$\chi^2$ Degrees of Freedom	2	1	3	1	1	1
$\chi^2$ P-value

Part a

Describe how the SBC statistic is calculated and verify the calculation of the SBC for the Negative Binomial model.

Part b

Perform a Likelihood ratio test to compare the ZM Poisson to the Poisson.

$H_0$ : population is a Poisson

$H_1$ : population is a ZM Poison (as printed)

Part c

Give ranges for the $\chi^2$ test p-values for each model.

Part d

What other criteria could be used to select a potential model?

Part e

Using the above scores and any other criteria, pick a preferred model and justify your choice.

Answer this question and see the worked solution