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Characterizations of some discrete distributions based on a variant of the Rao-Rubin condition. (English) Zbl 0611.62008

C. R. Rao’s damage model [On discrete distributions arising out of methods of ascertainment. Classical and contagious discrete distributions, Proc. Int. Symp., McGill Univ. Montreal/Can. 1963, 320-332 (1965)] is considered and characterizations of some discrete univariate and bivariate distributions are established using a variant of the Rao- Rubin condition.
In the univariate case our results may be thought of as extensions of results of G. P. Patil and M. V. Ratnaparkhi [Problems of damaged random variables and related characterizations. in G. P. Patil, S. Kotz and J. K. Ord (eds.): A modern course on statistical distributions in scientific work. Vol. 3: Characterizations and applications. NATO Adv. Study Inst. Ser., Ser. C 17 (1975; Zbl 0308.60003), pp. 255-270], R. S. Abdul-Razak [Power series distributions in mathematical statistics and applied probability. Ph. D. thesis, Penn. State Univ., Univ. Park, PA (1983)], and R. C. Gupta [Statistical distributions in scientific work, Vol. 4, Proc. NATO Adv. Study Inst., Trieste/Italy 1980, 341-347 (1981; Zbl 0475.62010)].

MSC:

62E10 Characterization and structure theory of statistical distributions
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References:

[1] Razak, R.S Abdul, Power series distribution in mathematical statistics and applied probability (1983)
[2] Gupta R.C., Statistical Distributions in Schientific Work 4 pp 341– (1981)
[3] Janardan K.G., A four urn model with predetermined strategy. Technical Report No. 73-1 (1973)
[4] Janardan K.G., Gujarat Statistical Review 5 pp 16– (1978)
[5] DOI: 10.1080/03610928208828374 · Zbl 0493.62015
[6] DOI: 10.1002/bimj.4710190202 · Zbl 0358.62016
[7] Panaretos J., Sankhya Ser 44 pp 415– (1982)
[8] Ratnaparkhi G.P.,, Statistical Distributions in Scientific Work 3 pp 255– (1975)
[9] Rao C.R., Classical and Contagious Discrete Distributions 3 pp 320– (1963)
[10] Rao C.R., Sankhya Ser 26 pp 294– (1964)
[11] DOI: 10.2307/3213471 · Zbl 0375.60021
[12] Dalwalker S., Sankhya Ser 34 pp 191– (1970)
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