CAS Exam MAS-I Fall 2018, Question 19
Study guide: Exam MAS-I
An actuary observes the following 20 losses for a select insurance policy:
\{20, 25, 36, 38, 42, 52, 55, 57, 65, 66, 69, 71, 72, 73, 74, 74, 74, 80, 81, 82\}
She believes the distribution which fits the data the best is loglogistic with the following probability density:
f(x; \gamma, \theta) = \frac{\gamma x^{\gamma-1}}{\theta^\gamma \left[1 + \left(\frac{x}{\theta}\right)^\gamma\right]^2}
She uses the 20^{\text{th}} and 80^{\text{th}} percentiles to estimate the two parameters of this distribution.
Calculate the estimated value of \theta.
- A) Less than 20
- B) At least 20, but less than 30
- C) At least 30, but less than 40
- D) At least 40, but less than 50
- E) At least 50
Answer this question and see the worked solution