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- W2161036356 abstract "Abstract Following Gupta and Wesolowski [1997. Uniform mixtures via posterior means. Ann. Inst. Statist. Math. 49, 171–180], in this work, under the condition X / U and U are independent, X / U has a B e ( p , q ) distribution, and given X the conditional expectation of a certain function of ( U , X ) is constant, we characterize the distribution of ( U , X ) . This problem is related to Lukacs type characterization, where both X and Y have to be gamma distributed with the same scale parameter, if both X and Y, and X / ( X + Y ) and X + Y are independent. Among others, we prove if q = 1 , and for some integer n ⩾ 1 , E ( ∑ i = 1 n a i ( U - X ) i | X ) = b , where a 1 , … , a n , b , are real constants such that a 1 2 + ⋯ + a n 2 ≠ 0 and b ≠ 0 , or for some real number n > 0 , E ( ( U - X ) n | X ) = b , where b > 0 is a constant, then the distribution of ( U , X ) can be determined." @default.
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- W2161036356 date "2007-09-01" @default.
- W2161036356 modified "2023-10-14" @default.
- W2161036356 title "On some characterizations of the mixture of gamma distributions" @default.
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- W2161036356 doi "https://doi.org/10.1016/j.jspi.2006.10.011" @default.
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