The exponentiated transmuted Weibull geometric distribution with application in survival analysis

ABSTRACT This article introduces a new generalization of the transmuted Weibull distribution introduced by Aryal and Tsokos in 2011. We refer to the new distribution as exponentiated transmuted Weibull geometric (ETWG) distribution. The new model contains 22 lifetime distributions as special cases such as the exponentiated Weibull geometric, complementary Weibull geometric, exponentiated transmuted Weibull, exponentiated Weibull, and Weibull distributions, among others. The properties of the new model are discussed and the maximum likelihood estimation is used to evaluate the parameters. Explicit expressions are derived for the moments and examine the order statistics. To examine the performance of our new model in fitting several data we use two real sets of data, censored and uncensored, and then compare the fitting of the new model with some nested and nonnested models, which provides the best fit to all of the data. A simulation has been performed to assess the behavior of the maximum likelihood estimates of the parameters under the finite samples. This model is capable of modeling various shapes of aging and failure criteria.

[1]  David Lindley,et al.  Fiducial Distributions and Bayes' Theorem , 1958 .

[2]  Robert King,et al.  Transmuted Modified Weibull Distribution: A Generalization of the Modified Weibull Probability Distribution , 2013 .

[3]  Gauss M. Cordeiro,et al.  The Kumaraswamy modified Weibull distribution: theory and applications , 2014 .

[4]  William T. Shaw,et al.  The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map , 2009, 0901.0434.

[5]  M. E. Ghitany,et al.  Marshall–Olkin extended weibull distribution and its application to censored data , 2005 .

[6]  Gauss M. Cordeiro,et al.  The beta modified Weibull distribution , 2010, Lifetime data analysis.

[7]  Gauss M. Cordeiro,et al.  The Kumaraswamy Pareto distribution , 2012, J. Stat. Theory Appl..

[8]  Min Wang.  A new three-parameter lifetime distribution and associated inference , 2013, 1308.4128.

[9]  G. Cordeiro,et al.  The Weibull-geometric distribution , 2008, 0809.2703.

[10]  A Compound Class of Geometric and Lifetimes Distributions , 2013 .

[11]  Pranab Kumar Sen,et al.  Statistical Theory and Applications , 1996 .

[12]  Elisa T. Lee,et al.  Statistical Methods for Survival Data Analysis , 1994, IEEE Transactions on Reliability.

[13]  Y. H. Abdelkader,et al.  Computing the moments of order statistics from nonidentical random variables , 2004 .

[14]  E. Mahmoudi,et al.  Exponentiated Weibull-Geometric Distribution and its Applications , 2012, 1206.4008.

[15]  W. J. Padgett,et al.  Inference for Reliability and Stress-Strength for a Scaled Burr Type X Distribution , 2001, Lifetime data analysis.

[16]  Chris P. Tsokos,et al.  Transmuted Weibull Distribution: A Generalization of theWeibull Probability Distribution , 2011 .

[17]  Z. A. Lomnicki,et al.  Mathematical Theory of Reliability , 1966 .

[18]  Ayman Alzaatreh,et al.  Weibull-Pareto Distribution and Its Applications , 2013 .

[19]  Gauss M. Cordeiro,et al.  The beta generalized exponential distribution , 2008, 0809.1889.

[20]  Maurizio Vichi,et al.  Statistical Methods and Applications , 2005 .

[21]  W. J. Padgett,et al.  A Bootstrap Control Chart for Weibull Percentiles , 2006, Qual. Reliab. Eng. Int..

[22]  Abd El Hady N. Ebraheim.  Exponentiated Transmuted Weibull Distribution A Generalization of the Weibull Distribution , 2014 .

[23]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[24]  G. S. Mudholkar,et al.  Exponentiated Weibull family for analyzing bathtub failure-rate data , 1993 .

[25]  W. Weibull.  A statistical theory of the strength of materials , 1939 .

[26]  Ahmed M. T. Abd El-Bar,et al.  A new three-parameter lifetime distribution , 2018, Int. J. Comput. Sci. Math..