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Transmuted Weibull distribution: a generalization of the Weibull probability distribution. (English) Zbl 1389.62150
Summary: In this article, the two parameter Weibull probability distribution is embedded in a larger family obtained by introducing an additional parameter. We generalize the two parameter Weibull distribution using the quadratic rank transmutation map studied by W. T. Shaw and I. R. C. Buckley [“The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map”, Preprint, arXiv:0901.0434] to develop a transmuted Weibull distribution. We provide a comprehensive description of the mathematical properties of the subject distribution along with its reliability behavior. The usefulness of the transmuted Weibull distribution for modeling reliability data is illustrated using real data.

MSC:
62N05 Reliability and life testing
90B25 Reliability, availability, maintenance, inspection in operations research
62F10 Point estimation
62E15 Exact distribution theory in statistics
60E05 Probability distributions: general theory
Software:
R
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References:
[1] Gokarna R. Aryal and Chris P. Tsokos. On the transmuted extreme value distribution with application. Nonlinear Analysis: Theory, Methods and Applications, 71:1401–1407, 2009. · Zbl 1238.60018
[2] R. Ihaka and R. Gentleman. R: A language for data analysis and graphics. Journal of Computational and Graphical Statistics, 5:299–314, 1996.
[3] Govinda Mudholkar, Deo Srivastava, and George Kollia. A generalization of the weibull distribution with application to the analysis of survival data. Journal of the American Statistical Association, 91(436):1575–1583, 1996. · Zbl 0881.62017
[4] Manal M. Nassar and Fathy H. Eissa. On the Exponentiated Weibull Distribution. Com- munications in Statistics - Theory and Methods, 32(7):1317–1336, 2003. Note that {\(\lambda\)} 1 therefore the upper limit of {\(\lambda\)} can be simply replaced by 1. REFERENCES102 · Zbl 1140.62308
[5] M. D. Nichols and W.J. Padgett. A bootstrap control chart for Weibull percentiles. Quality and Reliability Engineering International, 22:141–151, 2006.
[6] M. Pal, M. M. Ali, and J. Woo. On the exponentiated weibull distribution. Statistica., (2):139–147, 2006. · Zbl 1188.62111
[7] Hoang Pham and Chin-Diew Lai. On Recent Generalizations of the Weibull Distribution. IEEE Transactions on RELIABILITY, 56(3):454–458, 2007.
[8] C. P. Quesenberry and Jacqueline Kent. Selecting Among Probability Distributions Used in Reliability. Technometrics, 24(1):59–65, 1982.
[9] W. Shaw and I. Buckley. The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map.. Research report, 2007.
[10] M. Zaindin and Ammar M. Sarhan. Parameters Estimation of the Modified Weibull Distribution. Applied Mathematical Sciences, 3(11):541–550, 2009. · Zbl 1216.62034
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