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Identification of power distribution mixtures through regression of exponentials

机译:通过指数回归识别配电混合物

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Given two independent non-degenerate positive random variables X and Y, Lukacs (Ann Math Stat 26:319-324, 1955) proved that X/(X + Y) and X + Y are independent if and only if X and Y are gamma distributed with the same scale parameter. In this work, under the assumption X/U and U are independent, and X/U has a Be(p, q) distribution, we characterize the distribution of (U, X) by the condition E(h(U - X){pipe}X) = b, where h is allowed to be a linear combination of exponential functions. Since the assumption for X and U above is equivalent to X{pipe}U being Be(p, 1) scaled by U, hence our results can be viewed as identification of a power distribution mixture.
机译:给定两个独立的非简并正随机变量X和Y,Lukacs(Ann Math Stat 26:319-324,1955)证明,当且仅当X和Y为伽玛时,X /(X + Y)和X + Y是独立的以相同的比例参数分布。在这项工作中,假设X / U和U是独立的,并且X / U具有Be(p,q)分布,我们通过条件E(h(U-X)来表征(U,X)的分布{pipe} X)= b,其中h被允许为指数函数的线性组合。由于上面关于X和U的假设等效于X {pipe} U由Be缩放的Be(p,1),因此我们的结果可以看作是配电混合物的标识。

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