Characterizations of the Extended Geometric, Harris, Negative Binomial and Gamma Distributions

Details Characterizations of the Extended Geometric, Harris, Negative Binomial and Gamma Distributions Characterizations of the Extended Geometric, Harris, Negative Binomial and Gamma Distributions

2005-12-25

arxiv.org/abs/math/0512565v1

Mathematics

Statistics Theory

submitted, 10 pages, in pdf format

Scientific paper

Extended geometric distribution is defined and its mixture is characterized by the property of having completely monotone probability sequence. Also, convolution equations and probability generating functions are used to characterize extended geometric distributions. Further, some characterizations of Harris and negative binomial distributions based on probability generating functions are obtained. Relations between these distributions are derived and finally a gamma distribution is characterized in terms of its Laplace transform.

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