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Multivariate distributions of order ?

Author

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  • Philippou, Andreas N.
  • Antzoulakos, Demetris L.
  • Tripsiannis, Gregory A.

Abstract

Three multivariate distributions of order ? are introduced and studied. A multivariate negative binomial distribution of order ? is derived first, by means of an urn scheme, and two limiting cases of it are obtained next. They are, respectively, a multivariate Poisson distribution of order ? and a multivariate logarithmic series distribution of the same order. The probability generating functions, means variances and covariances of these distributions are obtained, and some further genesis schemes of them and interrelationships among them are also established. The present paper extends to the multivariate case the work of Philippou (1987) on multiparameter distributions of order ?. At the same time, several results of Aki (1985) on extended distributions of order ? are also generalized to the multivariate case.

Suggested Citation

  • Philippou, Andreas N. & Antzoulakos, Demetris L. & Tripsiannis, Gregory A., 1988. "Multivariate distributions of order ?," Statistics & Probability Letters, Elsevier, vol. 7(3), pages 207-216, December.
    • Handle: RePEc:eee:stapro:v:7:y:1988:i:3:p:207-216
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    Cited by:

    1. Qing Han & Sigeo Aki, 1999. "Joint Distributions of Runs in a Sequence of Multi-State Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(3), pages 419-447, September.

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