Sankhya: The Indian Journal of Statistics

1996, Volume 58, Series A, Pt. 1, pp. 135--141

ON CHARACTERIZATION OF CONTINUOUS DISTRIBUTIONS BY CONDITIONAL EXPECTION OF RECORD VALUES

By

M. FRANCO and  J. M. RUIZ, Universidad de Murcia

SUMMARY.  Let R0<R1<...<Rn<... be the upper record values from a population with continuous distribution function F. In this paper, we obtain the distribution function F from conditional expectation $E(h(R_{n-1})|R_n=x)$, where h is real, continuous and strictly monotonic function. We gave necessary and sufficient conditions so that any real function $\varphi(x)$ is equal to $E(h(R_{n-1})|R_n=x)$. Finally, we show some counterexamples for the necessity or/and sufficiency of assumed conditions, and different continuous distributions are also characterized using our results.

AMS (1980) subject classification.  62E05, 60E10.

Key words and phrases. Characterization, upper record values, record mean function, cumulative hazard function, regression.

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