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

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  • Attila Csenki

    (University of Bradford)

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.

Suggested Citation

  • Attila Csenki, 2015. "A Differential Equation for a Class of Discrete Lifetime Distributions with an Application in Reliability," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 647-660, September.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:3:d:10.1007_s11009-013-9385-0
    DOI: 10.1007/s11009-013-9385-0
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    References listed on IDEAS

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    1. Csenki, Attila, 2011. "On continuous lifetime distributions with polynomial failure rate with an application in reliability," Reliability Engineering and System Safety, Elsevier, vol. 96(11), pages 1587-1590.
    2. Sarhan, Ammar M. & Hamilton, David C. & Smith, Bruce & Kundu, Debasis, 2011. "The bivariate generalized linear failure rate distribution and its multivariate extension," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 644-654, January.
    3. Csenki, Attila, 2012. "Asymptotics for continuous lifetime distributions with polynomial failure rate with an application in reliability," Reliability Engineering and System Safety, Elsevier, vol. 102(C), pages 1-4.
    4. Yanyuan Ma & Marc Genton & Emanuel Parzen, 2011. "Asymptotic properties of sample quantiles of discrete distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 227-243, April.
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