On a characterization of lagrangian poisson and quasi-binomial distributions
Prem Chandra Consul · Communications in Statistics · 1975
Since the probability of success of an event appears to increase or decrease with Che number of successes or failures in most natural phenomena involving living beings, several authors have considered a auaoer of discrete probability aodels where the probability of success of an event is linearly dependent upon the number of successes. The Lagrangian Poiason distribution and the quasi-binomial, distribution are two such models. Considering a discrete model where the original observation is subjected to damage according to the quasi-binomial probability law a characterization of the Lagranglan-Poisson distribution is obtained if the resulting observation satisfies a given condition. Its converse is used to obtain a characterization of the quasi-binomial distribution.