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Invariance of linearity of regression and related characterizations of some classical discrete distributions
Authors:G. P. Patil  M. V. Ratnaparkhi
Affiliation:The Pennsylvania State University , University Park, Pennsylvania
Abstract:
Rao (1963) introduced what we call an additive damage model. In this model, original observation is subjected to damage according to a specified probability law by the survival distribution. In this paper, we consider a bivariate observation with second component subjected to damage. Using the invariance of linearity of regression of the first component on the second under the transition of the second component from the original to the damaged state, we obtain the characterizations of the Poisson, binomial and negative binomial distributions within the framework of the additive damage model.
Keywords:additive damage model  survival distribution  Poisson  binomial  negative binomial  damage to components
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