Notes on the sum and maximum of independent exponentially distributed random variables with different scale parameters
Probability
2013-07-16 v1
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.
Cite
@article{arxiv.1307.3945,
title = {Notes on the sum and maximum of independent exponentially distributed random variables with different scale parameters},
author = {Markus Bibinger},
journal= {arXiv preprint arXiv:1307.3945},
year = {2013}
}