A discrete distribution associated with a pure birth process |
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| Authors: | Konanur G Janardan |
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| Institution: | (1) Department of Mathematics, Eastern Michigan University, 48197 Ypsilanti, MI, USA |
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| Abstract: | A discrete distribution associated with a pure birth process starting with no individuals, with birth rates λ
n
=λ forn=0, 2, …,m−1 and λ
n
forn≥m is considered in this paper. The probability mass function is expressed in terms of an integral that is very convenient for
computing probabilities, moments, generating functions and others. Using this representation, the mean and the k-th factorial
moments of the distribution are obtained. Some nice characterizations of this distribution are also given. |
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| Keywords: | Birth process Continuous time Markov-chain Poisson Poisson-binomial Poisson-negative-binomial Over-(under-) dispersion Integral representation Oviposition evolution parasite |
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