Characterizations of Certain Statistical Distributions Based on Additive Damage Models Involving Rao-Rubin Condition and Some of Its Variants

This paper investigates the characterizations of certain discrete and continuous distributions within the framework of an additive damage model introduced by Rao. In this model, original observation is subjected to damage (under-reporting) according to a specified probability law. Using what is known as Rao-Rubin condition, it is shown that gamma distribution is the only distribution for the true observation if the under-reporting law is power function distribution. Using certain variations in the Rao-Rubin condition, major classical discrete distributions are further characterized. A few practical interpretations are offered when available.