Panaretos, John (1990): On the Duality of Certain Characterizations of the Exponential and the Geometric Distributions. Published in: Proceedings of the First International Symposium on Uncertainty Modeling and Analysis (1990): pp. 156160.

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Abstract
Let {N(t), t>0} be a homogeneous Poisson process with parameter λ=1. Let Z be a nonnegative random variable which is distributed independently of {N(t), t>0} according to a mixed game distribution. Xekalaki and Panaretos (1988) showed that the form of F (the mixing distribution) is uniquely determined by that of the distribution of N(Z). They also showed that certain characterizations of N(Z) can be derived through characterizations of F. In this paper it is demonstrated that through the above mentioned results a deeper insight is gained into the relationship of the distribution duals (geometricexponential and YulePareto). Two characterization theorems are also shown for the exponential distribution which can be thought of as variants of Govindarajulu's (1966) and Crawford's (1966) characterizations of the exponential distribution as the corresponding characterizing conditions are weaker than those used by them
Item Type:  MPRA Paper 

Original Title:  On the Duality of Certain Characterizations of the Exponential and the Geometric Distributions 
Language:  English 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General 
Item ID:  6259 
Depositing User:  J Panaretos 
Date Deposited:  13. Dec 2007 07:25 
Last Modified:  16. Feb 2013 13:24 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/6259 