TY - JOUR
T1 - Natural exponential families and generalized hypergeometric measures
AU - Lu, I. Li
AU - Richards, Donald St P.
PY - 2008/1
Y1 - 2008/1
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.
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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 -