A Differential Equation for a Class of Discrete Lifetime Distributions with an Application in Reliability

Attila Csenki ()
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Attila Csenki: University of Bradford

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 3, 647-660

Abstract: Abstract It is shown that the probability generating function of a lifetime random variable T on a finite lattice with polynomial failure rate satisfies a certain differential equation. The interrelationship with Markov chain theory is highlighted. The differential equation gives rise to a system of differential equations which, when inverted, can be used in the limit to express the polynomial coefficients in terms of the factorial moments of T. This then can be used to estimate the polynomial coefficients. Some special cases are worked through symbolically using Computer Algebra. A simulation study is used to validate the approach and to explore its potential in the reliability context.

Keywords: Polynomial failure rate; Probability generating function; Markov chain; Stirling numbers; Computer algebra; Point estimation; Reliability; 60J22; 90B25; 62M05; 65C50 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11009-013-9385-0

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