A characterization of conjugate priors in exponential families with application to inverse regression

2013 ◽  
Vol 83 (2) ◽  
pp. 650-654 ◽  
Author(s):  
Wei Luo ◽  
Naomi S. Altman
Keyword(s):  
Exponential Families ◽  
Inverse Regression ◽  
Conjugate Priors

A characterization of certain discrete exponential families

1996 ◽  
Vol 48 (3) ◽  
pp. 573-576 ◽  
Author(s):  
T. T. Nguyen ◽  
A. K. Gupta ◽  
Y. Wang
Keyword(s):  
Exponential Families

scholarly journals Credible Means are exact Bayesian for Exponential Families

1974 ◽  
Vol 8 (1) ◽  
pp. 77-90 ◽  
Author(s):  
William S. Jewell
Keyword(s):  
Least Squares ◽  
Unbiased Estimator ◽  
Exponential Families ◽  
Sufficient Statistic ◽  
Experience Rating ◽  
Conjugate Priors ◽  
Extended Sense ◽  
The Mean

AbstractThe credibility formula used in casualty insurance experience rating is known to be exact for certain prior-likelihood distributions, and is the minimum least-squares unbiased estimator for all others. We show that credibility is, in fact, exact for all simple exponential families where the mean is the sufficient statistic, and is also exact in an extended sense for all regular distributions with their natural conjugate priors where there is a fixed-dimensional sufficient statistic.

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.

Characterization of multinomial exponential families by generalized variance

2010 ◽  
Vol 80 (11-12) ◽  
pp. 939-944 ◽  
Author(s):  
Abdelaziz Ghribi ◽  
Afif Masmoudi
Keyword(s):  
Exponential Families ◽  
Generalized Variance

scholarly journals A martingale characterization of Pólya-Lundberg processes

2006 ◽  
Vol 43 (3) ◽  
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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