Linear Combination of Independent Exponential Random Variables

Kim-Hung Li () and Cheuk Ting Li ()
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Kim-Hung Li: Asian Cities Research Centre Ltd.
Cheuk Ting Li: University of California, Berkeley

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 1, 253-277

Abstract: Abstract 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.

Keywords: Affine combination; Erlang distribution; Hypoexponential distribution; Hermite interpolating polynomial; Matrix function; Recurrence relation; 65Q30; 65C50 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-018-9653-0

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