Exam MAS-I Practice Question 151

Study guide: Exam MAS-I

Auto claims are banded as small ( $Y = 1$ ), medium ( $Y = 2$ ) or large ( $Y = 3$ ). An actuary fits a proportional odds model

 $\ln\!\left(\frac{\gamma_j}{1 - \gamma_j}\right) = \theta_j + \beta x, \qquad \gamma_j = P(Y \le j), \quad j = 1, 2,$

where $x = 1$ for a commercial vehicle and $x = 0$ for a private one. The estimates are $\theta_1 = 0.5$ , $\theta_2 = 2.0$ and $\beta = -0.7$ .

Which of the following statements is correct?

A) At each cut-point, a commercial claim's odds of being at or below that band are about half a private claim's
B) Commercial claims are more likely than private claims to be small, since the coefficient on the commercial indicator is negative
C) Each band's probability for a commercial claim is the private claim's probability for that band multiplied by $e^{-0.7}$
D) The commercial-to-private odds ratio is larger at the second cut-point than at the first, because $\theta_2$ exceeds $\theta_1$
E) A private-vehicle claim is in the medium band with probability $e^{2.0}/(1 + e^{2.0}) = 0.881$ , read off the second cut-point

Concepts tested