Summary
In this paper, a new discrete distribution applicable for modeling discrete reliability and survival data is proposed. This distribution is a discrete version of the modified Weibull model obtained by Lai et al. (2003), and has increasing or bathtub shaped failure rate function. Some properties and characteristics of it are studied. The Weibull probability paper plot method and the maximum likelihood approach are considered to estimate its parameters. Finally, the initiated model and some other discrete distributions are fitted to two data sets of lifetimes, and are compared for their ability to describe the data.
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References
Aarset, M. V. (1987) How to identify bathtub hazard rate, IEEE Transactions on Reliability, 36, 106–108.
Aghababaei Jazi, M., Lai, C. D. and Alamatsaz, M. H. (2010) A discrete inverse Weibull distribution and estimation of its parameters, Statistical Methodology, 7, 121–132.
Barlow, R. E. and Proschan, F. (1981) Statistical Theory of Reliability and Life Testing, To Begin With, Silver Spring, Maryland.
Bebbington, M., Lai, C. D. and Zitikis, R. (2007) A flexible Weibull extension, Reliability Engineering and Systems Safety, 92, 719–726.
Bebbington, M., Lai, C. D. and Zitikis, R. (2008) Estimating the turning point of a bathtub-shaped failure distribution, Journal of Statistical Planning and Inference, 138, 1157–1166.
Bebbington, M., Lai, C. D., Murthy, D. N. P. and Zitikis, R. (2009) Modeling N and W shaped hazard rate functions without mixing distributions, Proceedings of the Institution of Mechanical Engineers, Part O, Journal of Risk and Reliability, 223, 59–69.
Davis, D. J. (1952) An analysis of some failure data, Journal of the American Statistical Association, 47, 113–150.
Jiang, R. (2010) Discrete competing risk model with application to modeling bus-motor failure data, Reliability Engineering and System Safety, 95, 981–988.
Jiang, R. and Murthy, D. N. P. (1995a) Graphicalrepresentation of two mixed Weibull distribution, IEEE Transactions on Reliability, 44, 477–488.
Jiang, R. and Murthy, D. N. P. (1995b) Reliability modeling involving two Weibull distributions, Reliability Engineering and Systems Safety, 47, 187–198.
Jiang, R. and Murthy, D. N. P. (1999) Exponentiated Weibull family: A graphical approach, IEEE Transactions on Reliability, 48, 68–72.
Krishna, H. and Pundir, P. S. (2009) Discrete Burr and discrete Pareto distributions, Statistical Methodology, 6, 177–188.
Lai, C. D., Xie, M. and Murthy, D. N. P. (2003) A modified Weibull distribution, IEEE Transactions on Reliability, 25, 33–37.
Lai, C. D. and Xie, M. (2006) Stochastic Aging and Dependence for Reliability, Springer, ISBN: 978-0-387-29742-2.
Nakagawa, T. and Osaki, S. (1975) Discrete Weibull distribution, IEEE Transactions on Reliability, 24, 300–301.
Roy, D. (2003) The discrete normal distribution, Communication in Statistics-Theory and Methods, 32, 1871–1883.
Roy, D. (2004) Discrete Rayleigh distribution, IEEE Transactions on Reliability, 53, 255–260.
Salvia, A. A. and Bollinger, R. C. (1982) On discrete hazard functions, IEEE Transactions on Reliability, R-31, 458–459.
Xie, M., Tang, Y. and Goh, T. N. (2002) A modified Weibull extension with bathtub-shaped failure rate function, Reliability Engineering and Systems Safety, 76, 279–285.
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Shafaei Nooghabi, M., Reza Mohtashami Borzadaran, G. & Hamid Rezaei Roknabadi, A. Discrete modified Weibull distribution. METRON 69, 207–222 (2011). https://doi.org/10.1007/BF03263557
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DOI: https://doi.org/10.1007/BF03263557