Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk

Appendix A Miscellaneous Definitions and List of Distributions

A.1 Indicator Function

The often used indicator symbol {⋅} is defined as

(A.1)

In addition on occasion we will also utilize {⋅}.

A.2 Gamma Function

The standard gamma function Γ(α) is defined as

(A.2)

A.3 Discrete Distributions

A.3.1 POISSON DISTRIBUTION

A Poisson distribution function is denoted as Poisson(λ). The random variable N has a Poisson distribution, denoted N ~ Poisson(λ), if its probability mass function is

(A.3)

for all k {0, 1,2,…}. Expectation, variance, and variational coefficient of a random variable N ~ Poisson(λ) are

(A.4)

A.3.2 BINOMIAL DISTRIBUTION

The Binomial distribution function is denoted as Binomial (n, p). The random variable N has a Binomial distribution, denoted ...