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Student Solutions Manual to Accompany Loss Models: From Data to Decisions, Fourth Edition by Gordon E. Willmot, Harry H. Panjer, Stuart A. Klugman

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CHAPTER 15

CHAPTER 15

15.1   SECTION 15.2

15.1 image. Let W = ln Y − ln 100 = ln(Y/100). Then y = 100ew and dy = 100ewdw. Thus,

image

which is a Pareto density with α = 12 and θ = 4.801121.

15.2

image

which is a gamma distribution with parameters 10 + γ and image image. The mean is image. For the mle:

image

for image. The two estimators are equal when γ = 0 and θ = ∞, which corresponds to π(α) = α−1, an improper prior.

15.3 (a) image

(b) Let

image

Then

and the solution is . Also,

and so .

(c)

which is a normal pdf with mean and variance ...

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