Notes on the sum and maximum of independent exponentially distributed random variables with different scale parameters

Markus Bibinger

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arXiv · 1307.3945

Notes on the sum and maximum of independent exponentially distributed random variables with different scale parameters

Markus Bibinger

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Abstract

We consider the distribution of the sum and the maximum of a collection of independent exponentially distributed random variables. The focus is laid on the explicit form of the density functions (pdf) of non-i.i.d. sequences. Those are recovered in a simple and direct way based on conditioning. A connection between the pdf and a representation of the convolution characteristic function as a linear combination of the single characteristic functions is drawn. It is demonstrated how the results on the pdf of order statistics and the convolution merge.

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Markus Bibinger. 2013-07-15. Notes on the sum and maximum of independent exponentially distributed random variables with different scale parameters. https://arxiv.org/abs/1307.3945

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