SOA Exam ASTAM Sample Question 8

Study guide: Exam ASTAM

The random variable X has distribution function F(x) where

F(x) = 1 - \exp(-2x)\left(x^2 + x + 1\right) \qquad x > 0

Part a

Derive the hazard rate function for this distribution.

Part b

Comment on the tail behaviour of this distribution, compared with the exponential distribution with the same mean

Part c

Derive the mean excess loss function for this distribution.

Part d

The distribution lies in the MDA of the GEV distribution, with parameter \xi. State with reasons whether \xi is greater than 0, equal to 0, or less than 0.

Answer this question and see the worked solution

Concepts tested

• Hazard Rate
• Mean Excess Loss
• Tail Weight
• Exponential Distribution
• Generalized Extreme Value Distribution

More questions from this set

• SOA Exam ASTAM Sample Question 7
• SOA Exam ASTAM Sample Question 9