TOWARDS A UNIFICATION OF CERTAIN CHARACTERIZATIONS BY CONDITIONAL EXPECTATIONS

CATERINA DIMAKI AND EVDOKIA XEKALAKI

Department of Statistics, Athens University of Economics and Business, 76 Patission St., Athens 104-34, Greece

(Received March 9, 1992; revised January 30, 1995)

Abstract. The paper presents a characterization of a general family of distributions by the form of the expectation of an appropriately truncated function of the random variable involved. The obtained result unifies results existing in the literature for specific distributions as well as new results that appear for the first time in this paper. A discrete version is also provided unifying existing characterizations of known discrete distributions.

Key words and phrases: Characterization, conditional expectation, Pareto distribution, exponential distribution, Weibull distribution, Burr distribution, power function distribution, beta distribution, uniform distribution, geometric distribution, Yule distribution, Waring distribution.