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Canonical Expansion of a Mixed Bivariate Distribution with Negative Binomial and Gamma Marginals

✍ Scribed by P.A. Lee

Publisher: Elsevier Science
Year: 1979
Tongue: English
Weight: 441 KB
Volume: 307
Category: Article
ISSN: 0016-0032
DOI: 10.1016/0016-0032(79)90002-4

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✦ Synopsis

For the following mixed bivariate probability distribution between a discrete random variable X and a continuous random variable A: h(x, A) = (Pq)"p"A"-' exp {-A(@ +p)}LF'(-Aqq

)/IYcw), where a, p>o, O<p=l-q<l, x=0,1,2 ,..., O<A<y and 21: h(x, A)dA = 1, a canonical expansion is obtained in terms of the Laguerre and Meixner orthogonal polynomials. The chance mechanisms giving rise to this mixed bivariate distribution are also discussed.

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