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A differential equation for a class of discrete lifetime distributions with an application in reliability: A demonstration of the utility of computer algebra
Csenki, Attila
Csenki, Attila
Publication Date
2015-09
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© 2015 Springer. Full-text reproduced in accordance with the publisher’s
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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.
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Accepted Manuscript
Citation
Csenki A (2015) A differential equation for a class of discrete lifetime distributions with
an application in reliability: A demonstration of the utility of computer algebra. Methodology and
Computing in Applied Probability. 17(3): 647-660.
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Article