Abstract
There are some characterizations of the exponential distribution based on the relation of the maximum of two observations expressed as linear combination of the two observations. In this paper some generalizations of this known characterization of the exponential distribution using the relations between the maximum and minimum of independent and identically distributed random variables having absolutely continuous (with respect to Lebesgue measure) distribution function will be presented.
Highlights
There are some characterizations of the exponential distribution based on the relation of the maximum of two observations expressed as linear combination of the two observations
Many times the researcher wants to verify whether the data that she/he has obtained belong to a certain family of distribution
In this paper some generalizations of this characterization of the exponential distribution based on the relation between maximum and minimum of n (≥ 2) independent and identically distributed continuous random variables are derived
Summary
Many times the researcher wants to verify whether the data that she/he has obtained belong to a certain family of distribution. In this paper some generalizations of this known characterization of the exponential distribution using the relations between the maximum and minimum of n (≥ 2) independent and identically distributed random variables having absolutely continuous (with respect to Lebesgue measure) distribution function will be presented. There are many characterizations of the exponential distribution using ordered random variables. Ferguson (1967) characterized the exponential distribution using the regression properties of the first two order statistics.
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