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For characterization of negative exponential distribution one needs
any arbitrary non-constant function only in place of approaches such as
identical distributions, absolute continuity, constant regression of order
statistics, continuity and linear regression of order statistics,
non-degeneracy etc. available in the literature. Path breaking different
approach for characterization of negative exponential distribution through
expectation of non-constant function of random variable is obtained. An example
is given for illustrative purpose.
For the characterization of the power function distribution, one needs any arbitrary non constant function only in place of independence of suitable function of order statistics, linear relation of conditional expectation, recurrence relations between expectations of function of order statistics, distributional properties of exponential distribution, record valves, lower record statistics, product of order statistics and Lorenz curve, etc. available in the literature. The goal of this research is not to give a different path-breaking approach for the characterization of power function distribution through the expectation of non constant function of random variable and provide a method to characterize the power function distribution as remark. Examples are given for the illustrative purpose.