Question

Which of the following statements are true?

- The mean excess loss function for an empirical distribution is continuous.

- The mean excess loss function for an exponential distribution is constant.

- If exists, the mean excess loss function for a Pareto distribution is decreasing.

I and II only

II and III only

I only

II only

III only

Answer 1

II only

Empirical distribution function is discontinuous (it corresponds to a discrete random variable) and then the mean excess loss function is also discontinuous.

The increasing mean excess loss function is an indication that the Pareto distribution is a heavy tailed distribution. In general, an increasing mean excess loss function is an indication of a heavy tailed distribution.