ON THE UNIMODALITY OF THE GENERALIZED NEGATIVE BINOMIAL DISTRIBUTION

P. C. Consul; F. Famoye

doi:10.1111/j.1467-9574.1986.tb01510.x

ON THE UNIMODALITY OF THE GENERALIZED NEGATIVE BINOMIAL DISTRIBUTION

P. C. Consul, F. Famoye

Statistics, Actuarial & Data Sciences

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Abstract. It is shown that the generalized negative binomial distribution which is useful in random walks, queueing theory and branching processes is unimodal. When nθ(1 –θ)β‐1 > 1, the mode is not at the point x= 0 and for that case, the lower and the upper bounds of the mode are obtained.

Original language	English
Pages (from-to)	141-144
Number of pages	4
Journal	Statistica Neerlandica
Volume	40
Issue number	3
DOIs	https://doi.org/10.1111/j.1467-9574.1986.tb01510.x
State	Published - Sep 1986

Keywords

Lagrangian probability distributions
bounds for mode
branching processes
random walks
self—decomposable distributions
unimodality

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10.1111/j.1467-9574.1986.tb01510.x

Cite this

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N2 - Abstract. It is shown that the generalized negative binomial distribution which is useful in random walks, queueing theory and branching processes is unimodal. When nθ(1 –θ)β‐1 > 1, the mode is not at the point x= 0 and for that case, the lower and the upper bounds of the mode are obtained.

AB - Abstract. It is shown that the generalized negative binomial distribution which is useful in random walks, queueing theory and branching processes is unimodal. When nθ(1 –θ)β‐1 > 1, the mode is not at the point x= 0 and for that case, the lower and the upper bounds of the mode are obtained.

KW - Lagrangian probability distributions

KW - bounds for mode

KW - branching processes

KW - random walks

KW - self—decomposable distributions

KW - unimodality

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ER -

ON THE UNIMODALITY OF THE GENERALIZED NEGATIVE BINOMIAL DISTRIBUTION

Abstract

Keywords

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