On Characterization of Multiparameter Exponential Family and of some Irregular Families of Distributions

1996 ◽  
Vol 46 (1-2) ◽  
pp. 9-22
Author(s):  
P. N. Jani ◽  
A. K. Singh
Keyword(s):  
Exponential Family ◽  
Exponential Families ◽  
Exponential Family Of Distributions ◽  
Multivariate Exponential ◽  
Family Of Distributions

A characterization through moments given by Khatri (1959) for p.s.d. and by Jani (1993) for one-parameter exponential family has been extended for the wider class viz. multiparameter and multivariate exponential family of distributions. The same problem has beon studied also for some non-exponential families where the support contains the parameter(s), called irregular families of distributions.

A Characterization of One-Parameter Exponential Family of Distributions

1993 ◽  
Vol 43 (3-4) ◽  
pp. 253-256 ◽  
Author(s):  
P. N. Jani
Keyword(s):  
Power Series ◽  
Exponential Family ◽  
Exponential Family Of Distributions ◽  
Power Series Distributions ◽  
Family Of Distributions

A characterization through moments given by Khatri (1959) for power series distributions (p. s. d.) and by Ahsanullah (1992) for modified power series distributions (m.p.s.d.) bas been extended for the wider class viz one-parameter exponential family of distributions.

scholarly journals Asymptotic approximations to the Bayes posterior risk

1990 ◽  
Vol 3 (2) ◽  
pp. 99-116
Author(s):  
Toufik Zoubeidi
Keyword(s):  
Parameter Space ◽  
Exponential Family ◽  
Distribution Functions ◽  
Independent Random Variables ◽  
Asymptotic Approximations ◽  
Prior Density ◽  
Posterior Probabilities ◽  
Exponential Family Of Distributions ◽  
Family Of Distributions ◽  
Convex Subsets

Suppose that, given ω=(ω1,ω2)∈ℜ2, X1,X2,… and Y1,Y2,… are independent random variables and their respective distribution functions Gω1 and Gω2 belong to a one parameter exponential family of distributions. We derive approximations to the posterior probabilities of ω lying in closed convex subsets of the parameter space under a general prior density. Using this, we then approximate the Bayes posterior risk for testing the hypotheses H0:ω∈Ω1 versus H1:ω∈Ω2 using a zero-one loss function, where Ω1 and Ω2 are disjoint closed convex subsets of the parameter space.

scholarly journals A martingale characterization of Pólya-Lundberg processes

2006 ◽  
Vol 43 (03) ◽  
pp. 741-754 ◽  
Author(s):  
Birgit Niese
Keyword(s):  
Poisson Process ◽  
Exponential Family ◽  
Exponential Families ◽  
Counting Processes ◽  
Mixed Poisson Process ◽  
Martingale Characterization

We study exponential families within the class of counting processes and show that a mixed Poisson process belongs to an exponential family if and only if it is either a Poisson process or has a gamma structure distribution. This property can be expressed via exponential martingales.

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