caa a22 4500 605519609 CHVBK 20210128100731.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s11009-013-9385-0 doi (NATIONALLICENCE)springer-10.1007/s11009-013-9385-0 Csenki Attila School of Computing, Informatics and Media, University of Bradford, Bradford, UK aut A Differential Equation for a Class of Discrete Lifetime Distributions with an Application in Reliability [Elektronische Daten] A Demonstration of the Utility of Computer Algebra [Attila Csenki] 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. Springer Science+Business Media New York, 2013 Polynomial failure rate nationallicence Probability generating function nationallicence Markov chain nationallicence Stirling numbers nationallicence Computer algebra nationallicence Point estimation nationallicence Reliability nationallicence Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/3(2015-09-01), 647-660 1387-5841 17:3<647 2015 17 11009 https://doi.org/10.1007/s11009-013-9385-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9385-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Csenki Attila School of Computing, Informatics and Media, University of Bradford, Bradford, UK aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/3(2015-09-01), 647-660 1387-5841 17:3<647 2015 17 11009