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Exponentiated Transmuted Weibull Distribution A Generalization of the Weibull Distribution

Authors: Abd El Hady N. Ebraheim


This paper introduces a new generalization of the two parameter Weibull distribution. To this end, the quadratic rank transmutation map has been used. This new distribution is named exponentiated transmuted Weibull (ETW) distribution. The ETW distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, eleven lifetime distributions such as the Weibull, exponentiated Weibull, Rayleigh and exponential distributions, among others follow as special cases. The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters. Explicit expressions are derived for the quantiles. The moments of the distribution are derived, and the order statistics are examined.

Keywords: exponentiated, inversion method, maximum likelihood estimation, transmutation map

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[1] W. T. Shaw and I. R. Buckley, The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. Research report, 2007.
[2] G. R. Aryal, and C. P. Tsokos, "On the transmuted extreme value distribution with application,” Nonlinear Analysis: Theory, Methods & Applications, vol.71, no. 12, pp. 1401-1407, 2009.
[3] G. R. Aryal, and C. P. Tsokos, "Transmuted Weibull Distribution: A Generalization of the Weibull Probability Distribution,” European Journal of Pure & Applied Mathematics, vol. 4, no. 2, 2011.
[4] M. S. Khan, and R. King, "Transmuted Modified Weibull Distribution: A Generalization of the Modified Weibull Probability Distribution,” European Journal of Pure & Applied Mathematics, vol.6, no. 1, 2013.
[5] G. R. Aryal, "Transmuted log-logistic distribution,” Journal of Statistics Applications & Probability, vol. 2, no.1, pp. 11-20, 2013.
[6] W. Weibull, "A statistical theory of the strength of material,” Ingeniors Vetenskapa Acadamiens Handligar, pp. 1–45. 1939.
[7] D. P. Murthy, M. Xie, and R. Jiang, Weibull Model. John Wiley & Sons. 2004.
[8] G. S. Mudholkar, and D. K. Srivastava, "Exponentiated Weibull family for analyzing bathtub failure-rate data,” IEEE Transactions on Reliability, vol. 42, no. 2, pp. 299-302, 1993.
[9] J. G. Surles, and W. J. Padgett, "Inference for reliability and stress-strength for a scaled Burr type X distribution,” Lifetime Data Analysis, vol.7, no.2, pp. 187-200, 2001.
[10] R. C. Gupta, P. L. Gupta, and R. D. Gupta, "Modeling failure time data by Lehman alternatives,” Communications in Statistics-Theory and methods, vol.27, no. 4, pp. 887-904, 1998‏.
[11] A. M. Law, W. D. Kelton, and W. D. Kelton, Simulation Modeling and Analysis (Vol. 2). New York: McGraw-Hill, 1991.
[12] M. Zaindin, and A. M. Sarhan, "Parameters estimation of the Modified Weibull distribution,” Applied Mathematical Sciences, vol. 3, no. 11, pp. 541-550, 2009.