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The characteristic function of order statistics
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[QUOTE="EngWiPy, post: 5987036, member: 157016"] Suppose that ##Y=\sum_{k=1}^KX_{(k)}##, where ##X_{(1)}\leq X_{(2)}\leq\cdots X_{(N)}## and (##N\geq K##). I want to find the characteristic function of ##Y## as [tex]\phi(jvY)=E\left[e^{jvY}\right]=E\left[e^{jv\sum_{k=1}^KX_{(k)}}\right][/tex] In the case where ##\{X\}## are i.i.d random variables, the above characteristic function will be [tex]\phi(jvY)=\prod_{k=1}^K\phi(jvX_k)[/tex] but when the random variables are ordered, they are no longer independent. How can the characteristic function be found in this case? [/QUOTE]
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The characteristic function of order statistics
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