# Multivariate negative binomial distributions generated by multivariate exponential distributions

Applicationes Mathematicae (1999)

- Volume: 25, Issue: 4, page 463-472
- ISSN: 1233-7234

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topKopociński, Bolesław. "Multivariate negative binomial distributions generated by multivariate exponential distributions." Applicationes Mathematicae 25.4 (1999): 463-472. <http://eudml.org/doc/219220>.

@article{Kopociński1999,

abstract = {We define a multivariate negative binomial distribution (MVNB) as a bivariate Poisson distribution function mixed with a multivariate exponential (MVE) distribution. We focus on the class of MVNB distributions generated by Marshall-Olkin MVE distributions. For simplicity of notation we analyze in detail the class of bivariate (BVNB) distributions. In applications the standard data from [2] and [7] and data concerning parasites of birds from [4] are used.},

author = {Kopociński, Bolesław},

journal = {Applicationes Mathematicae},

keywords = {bivariate geometrical distribution; multivariate exponential distribution; multivariate negative binomial distribution},

language = {eng},

number = {4},

pages = {463-472},

title = {Multivariate negative binomial distributions generated by multivariate exponential distributions},

url = {http://eudml.org/doc/219220},

volume = {25},

year = {1999},

}

TY - JOUR

AU - Kopociński, Bolesław

TI - Multivariate negative binomial distributions generated by multivariate exponential distributions

JO - Applicationes Mathematicae

PY - 1999

VL - 25

IS - 4

SP - 463

EP - 472

AB - We define a multivariate negative binomial distribution (MVNB) as a bivariate Poisson distribution function mixed with a multivariate exponential (MVE) distribution. We focus on the class of MVNB distributions generated by Marshall-Olkin MVE distributions. For simplicity of notation we analyze in detail the class of bivariate (BVNB) distributions. In applications the standard data from [2] and [7] and data concerning parasites of birds from [4] are used.

LA - eng

KW - bivariate geometrical distribution; multivariate exponential distribution; multivariate negative binomial distribution

UR - http://eudml.org/doc/219220

ER -

## References

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- [2] C. B. Edwards and J. Gurland, A class of distributions applicable to accidents, J. Amer. Statist. Assoc. 56 (1961), 503-517. Zbl0201.52805
- [3] I. Kopocińska, B. Kopociński and A. Okulewicz, Mixed negative binomial distributions in analysis of the number of parasitic nematodes in blackbird (Turdus merula L.), in: Proceedings of Third National Conference on Applications of Mathematics to Biology and Medicine (Mądralin, 1997), 25-31.
- [4] B. Kopociński, E. Lonc and M. Modrzejewska, Fitting a modified binomial model, to distribution of avian lice Phthiraptea: Mellophaga) parasiting on pheasant Phasianus colchicus L.), Acta Parasitologica 43 (1988), 81-85.
- [5] E. Lonc, A. Okulewicz and I. Kopocińska, Estimation of distribution parameters of some avian parasites, Wiad. Parazytol. 43 (1997), 185-193.
- [6] A. W. Marshall and I. Olkin, A multivariate exponential distribution, J. Amer. Statist. Assoc. 62 (1967), 30-44.
- [7] K. Subrahmaniam and K. Subrahmaniam, On the estimation of the parameters in the bivariate negative binomial distribution, J. Roy. Statist. Soc. 35 (1973), 131-146. Zbl0281.62035

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