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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 5

CHAPTER 5 SOLUTIONS

5.1   SECTION 5.2

5.1 image. This is the cdf of the Pareto distribution. The pdf is image.

5.2 After three years, values are inflated by 1.331. Let X be the 1995 variable and Y = 1.331X be the 1998 variable. We want

Pr(Y > 500) = Pr(X > 500/1.331) = Pr(X > 376).

From the given information we have Pr(X > 350) = 0.55 and Pr(X > 400) = 0.50. Therefore, the desired probability must be between these two values.

5.3 Inverse:

image

This is the inverse Pareto distribution with τ = α and θ = 1/θ. Transformed: image. This is the Burr distribution with α = α, γ = τ, and θ = θ1/τ. Inverse transformed:

image

This is the inverse Burr distribution with τ = α, γ = τ and θ = θ−1/τ.

5.4

image

This is the loglogistic distribution with γ unchanged and θ = 1/θ.

5.5

image

which is the cdf of another lognormal ...

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