Compound distribution

A compound distribution is a combination of distributions that results in a continuous mixture distribution. This mixture distribution is also referred to as a compound distribution. The negative binomial distribution is an example of a compound distribution, where the mean is multiplied by n^2/(n-1*s) and the shape parameter remains the same.From: Performance Evaluation of Computer and Communication Systems [2019], The Weibull Distribution [2019], Optimal definition of the limit of detection (LOD) in detecting genetically modified grains from heterogeneous grain lots [2019]

The topology of stream networks

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Published in Richard J. Chorley, Spatial Analysis in Geomorphology, 2019

A. Werritty

This can be regarded as a compound distribution which is the product of the probability that streams of order ω have v links, and the probability that v links have a length ℒ. Symbolically this may be written as p(ℒ;ω, NΩ)= ∑vf(v;ω, NΩ)g(ℒ;v,ω, NΩ)(14)

Optimal definition of the limit of detection (LOD) in detecting genetically modified grains from heterogeneous grain lots

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Published in Quality Technology & Quantitative Management, 2019

Kohji Yamamura, Junichi Mano, Hiroyuki Shibaike

Then, the number of GM grains (Z) in the subsample is given by a compound distribution (i.e. a stopped-sum distribution by the terminology of Johnson, Kotz, and Kemp [2005]): a negative binomial distribution that is compounded with a Bernoulli distribution of the parameter n2/(n1s). The number of GM grains (Z) in the subsample is alternatively given by a mixture distribution: a mixture binomial distribution where the number of trials (Y) follows a negative binomial distribution. The compound distribution and the mixture distribution yield the same distribution: the negative binomial distribution where the mean is multiplied by n2/(n1s) while the shape parameter is the same.

Compound distribution

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The topology of stream networks

Optimal definition of the limit of detection (LOD) in detecting genetically modified grains from heterogeneous grain lots