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Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk by Pavel V. Shevchenko, Gareth W. Peters

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APPENDIXA

Miscellaneous Definitions and List of Distributions

A.1 Indicator Function

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

images

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

A.2 Gamma Function

The standard gamma function Γ(α) is defined as

images

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

images

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

images

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 ...

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