Student Solutions Manual to Accompany Loss Models: From Data to Decisions, Fourth Edition

CHAPTER 7

CHAPTER 7 SOLUTIONS

7.1   SECTION 7.1

7.1 Poisson: .

Negative binomial: .

Binomial: .

7.2 The geometric–geometric distribution has pgf

The Bernoulli–geometric distribution has pgf

The ZM geometric distribution has pgf

In P_BG(z), replace 1 − q with (1 + β₁)⁻¹ and replace β with β₂(1 + β₁) to see that it matches P_GG(z). It is clear that the new parameters will stay within the allowed ranges.

In P_GG(z), replace q with (1 − p₀)(1 + β*)/β* and replace β with β*. Some algebra leads to P_ZMG(z).

7.3 The binomial–geometric distribution has pgf

The negative binomial–geometric distribution has pgf

In the binomial–geometric pgf, replace m with r, β(1 − q) with β₂, and β with (1 + β₁)