Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk

APPENDIXA

Miscellaneous Definitions and List of Distributions

A.1 Indicator Function

The often used indicator symbol _{.} is defined as

In addition on occasion we will also utilise [·].

A.2 Gamma Function

The standard gamma function Γ(α) is defined as

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 as N ~ Poisson(λ), if its probability mass function is

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

A.3.2 BINOMIAL DISTRIBUTION

The Binomial distribution function is denoted as Binomial(n, p). The random variable N has a Binomial distribution, denoted as N ~ Binomial(n, p), if its probability mass function is

for all k ∈ {0, 1, 2, . . . , n}. Expectation, variance and variational coefficient of a ...