TY - JOUR

T1 - Natural exponential families and generalized hypergeometric measures

AU - Lu, I. Li

AU - Richards, Donald St P.

PY - 2008/1/1

Y1 - 2008/1/1

N2 - Let be a positive Borel measure on n and pFq(a1, ap; b1, bq; s) be a generalized hypergeometric series. We define a generalized hypergeometric measure, p,q:=pFq(a1, ap; b1, bq;), as a series of convolution powers of the measure , and we investigate classes of probability distributions which are expressible as such a measure. We show that the Kemp (1968) family of distributions is an example of p,q in which is a Dirac measure on . For the case in which is a Dirac measure on n, we relate p,q to the diagonal natural exponential families classified by Bar-Lev et al. (1994). For pq, we show that certain measures p,q can be expressed as the convolution of a sequence of independent multi-dimensional Bernoulli trials. For p=q, q+1, we show that the measures p,q are mixture measures with the Dufresne and Poisson-stopped-sum probability distributions as their mixing measures.

AB - Let be a positive Borel measure on n and pFq(a1, ap; b1, bq; s) be a generalized hypergeometric series. We define a generalized hypergeometric measure, p,q:=pFq(a1, ap; b1, bq;), as a series of convolution powers of the measure , and we investigate classes of probability distributions which are expressible as such a measure. We show that the Kemp (1968) family of distributions is an example of p,q in which is a Dirac measure on . For the case in which is a Dirac measure on n, we relate p,q to the diagonal natural exponential families classified by Bar-Lev et al. (1994). For pq, we show that certain measures p,q can be expressed as the convolution of a sequence of independent multi-dimensional Bernoulli trials. For p=q, q+1, we show that the measures p,q are mixture measures with the Dufresne and Poisson-stopped-sum probability distributions as their mixing measures.

UR - http://www.scopus.com/inward/record.url?scp=46349108577&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=46349108577&partnerID=8YFLogxK

U2 - 10.1080/03610920801968897

DO - 10.1080/03610920801968897

M3 - Article

AN - SCOPUS:46349108577

VL - 37

SP - 2472

EP - 2487

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 16

ER -