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A note on the generalized Rao–Rubin condition and characterization of certain discrete distributions

Published online by Cambridge University Press:  14 July 2016

Sheela Talwalker
Sheela Talwalker*
Affiliation:
CIBA-GEIGY Research Centre, Bombay
*
∗Postal address: CIBA-GEIGY Research Centre, Aarey Road, Goregaon East, P. B. 9002, Bombay 400 063, India.
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Abstract

Assuming that the original observation from a discrete distribution is subject to damage according to a binomial probability law, it is shown here that a class of discrete distributions consisting of binomial, Poisson and mixed Poisson distributions, is characterized by the generalized Rao–Rubin condition 0 <π, π′ < 1 are constants. Y denotes the resulting or observed random variable, taking the values r = 0, 1, 2, ….

Keywords

DISCRETEDISTRIBUTIONBINOMIALPOISSONMIXED POISSONBINOMIAL DAMAGE MODELRESULTING RANDOM VARIABLEGENERALIZED RAO–RUBIN CONDITIONCHARACTERIZATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 563 - 569
Copyright
Copyright © Applied Probability Trust 1980 

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References

Rao, C. R. (1963) On discrete distributions arising out of methods of ascertainment. Proc. Internat. Symp. Classical and Contagious Discrete Distributions, ed. Patil, G. P. Pergamon Press, Oxford.Google Scholar
Rao, C. R. and Rubin, H. (1964) On a characterization of the Poisson distribution. Sankhya A 26, 295–298.Google Scholar
Shanbhag, D. N. (1974) An elementary proof for the Rao–Rubin characterization of the Poisson distribution. J. Appl. Prob. 11, 211–215.CrossRefGoogle Scholar
Shanbhag, D. N. (1977) An extension of the Rao–Rubin characterization. J. Appl. Prob. 14, 640–646.CrossRefGoogle Scholar
Talwalker, S. (1975) Models in medicine and toxicology. In Statistical Distributions in Scientific Work, Vol. 2: Model Building and Model Selection , ed. Patil, G. P., Kotz, S. and Ord, J. K., Riedel, Dordrecht.Google Scholar