Linear Combination of Independent Exponential Random Variables

  • Kim-Hung LiEmail author
  • Cheuk Ting Li


In this paper we prove a recursive identity for the cumulative distribution function of a linear combination of independent exponential random variables. The result is then extended to probability density function, expected value of functions of a linear combination of independent exponential random variables, and other functions. Our goal is on the exact and approximate calculation of the above mentioned functions and expected values. We study this computational problem from different views, namely as a Hermite interpolation problem, and as a matrix function evaluation problem. Examples are presented to illustrate the applicability and performance of the methods.


Affine combination Erlang distribution Hypoexponential distribution Hermite interpolating polynomial Matrix function Recurrence relation 

Mathematics Subject Classification (2010)

65Q30 65C50 


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The work of the second author was done when he was with the Department of Electrical Engineering, Stanford University, USA.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Asian Cities Research Centre Ltd.Win PlazaHong Kong
  2. 2.Department of Electrical Engineering and Computer SciencesUniversity of California, BerkeleyBerkeleyUSA

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