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On Characterizing Probability Distributions by Conditional Expectation of Two Order Statistics |
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PP: 323-328 |
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doi:10.18576/msl/050315
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Author(s) |
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Haseeb Athar,
Zubdah-e-Noor,
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Abstract |
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| The order statistics have been extensively studied in the literature to characterize some particular distributions as well as
family of distributions. The problem of characterizing distributions through conditional expectation of adjacent and non-adjacent order
statistics has been of increasing interest due to its several applications. Several approaches are available in literature. In this paper,
two general classes of distributions F(x) = 1−e−ah(x) and F(x) = 1−[ah(x)+b]c, where h(x) is a continuous, differentiable and
monotonic function of xe (a,b ) have been characterized through the conditional expectation of kth power of difference of two order
statistics. Further, several deductions and particular cases are discussed. |
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