Transmuted Generalized Power Weibull Distribution
Keywords:
Reliability models, generalized power Weibull distribution, moment estimation, simulation, maximum likelihood estimationAbstract
This paper introduces the transmuted generalized power Weibull distribution by using the quadratic rank transmutation map technique (QRTM) and derive some of its structural properties. This paper formulates the expressions for the moments and probability weighted moments. The method of maximum likelihood is used for estimating the model parameters and evaluate the performance of MLE using simulation. An application to data on anxiety is discussed to illustrate the flexibility of the new distribution.
References
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Aryal GR, Tsokos CP. Transmuted Weibull distribution: A generalization of the Weibull probability distribution. Eur J Pure Appl Math. 2011; 4: 89-102.
Ashour SK, Eltehiwy MA. Transmuted Lomax distribution. Am J Appl Math Stat. 2013; 1: 121-127.
Elbatal I, Aryal G. On the Transmuted Additive Weibull distribution. Aust J Stat. 2013; 42: 117-132.
Khan MS, King R, Transmuted modified Weibull distribution: A generalization of the modified Weibull probability distribution. Eur J Pure Appl Math. 2013a; 6: 66-88.
Khan MS, King R. Transmuted generalized inverse Weibull distribution. J Appl Statist Sci 2013b; 20: 15-32.
Khan MS, King R. A New Class of transmuted inverse Weibull distribution for reliability analysis. Am J Math Manag Sc. 2014; 33: 261-286.
Khan MS, King R, Hudson I. Characterizations of the transmuted inverse Weibull distribution. ANZIAM J. 2014; 55: 197-217.
Khan MS, King R, Hudson I. Transmuted Weibull distribution properties and estimation. Comm Stat Theor Meth. 2017; 46: 5394-5418.
Marcelo B, Indranil G, Gauss MC. General results for the transmuted family of distributions and new models. J Probab Stat. 2016: 1-12.
Merovci F. Transmuted Rayleigh distribution. Aust J Stat. 2013; 42: 21-31.
Nikulin M, Haghighi F. A chi-squared test for the generalized power Weibull family for the head-and-neck cancer censored data. J Math Sci. 2006; 133: 1333-1341.
Nikulin M, Haghighi F. On the power generalized Weibull family: Model for cancer censored data, METRON. Int J Stat. 2009; 67: 75-86.
Olver FWJ, Lozier DM, Boisvert RF, Clark CW. NIST Handbook of Mathematical Functions. New York: Cambridge University Press; 2010.
R Core Team. R: A language and environment for statistical computing. Austria: the R Foundation for Statistical Computing; 2013.
Shaw W, Buckley I. The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. Proceeding of IMA Computational Finance Conference; 2007 March 23; London.
Smithson M, Verkuilen J. A better lemon-squeezer? Maximum likelihood regression with beta- distribuited dependent variables. Psycholog Meth. 2006; 11: 54-71.
Yuzhu T, Maozai T, Qianqian Zhu. Transmuted linear exponential distribution: A new generalization of the linear exponential distribution. Comm Stat Simulat Comput. 2014; 43: 2661-2677.
Aryal GR, Tsokos CP. Transmuted Weibull distribution: A generalization of the Weibull probability distribution. Eur J Pure Appl Math. 2011; 4: 89-102.
Ashour SK, Eltehiwy MA. Transmuted Lomax distribution. Am J Appl Math Stat. 2013; 1: 121-127.
Elbatal I, Aryal G. On the Transmuted Additive Weibull distribution. Aust J Stat. 2013; 42: 117-132.
Khan MS, King R, Transmuted modified Weibull distribution: A generalization of the modified Weibull probability distribution. Eur J Pure Appl Math. 2013a; 6: 66-88.
Khan MS, King R. Transmuted generalized inverse Weibull distribution. J Appl Statist Sci 2013b; 20: 15-32.
Khan MS, King R. A New Class of transmuted inverse Weibull distribution for reliability analysis. Am J Math Manag Sc. 2014; 33: 261-286.
Khan MS, King R, Hudson I. Characterizations of the transmuted inverse Weibull distribution. ANZIAM J. 2014; 55: 197-217.
Khan MS, King R, Hudson I. Transmuted Weibull distribution properties and estimation. Comm Stat Theor Meth. 2017; 46: 5394-5418.
Marcelo B, Indranil G, Gauss MC. General results for the transmuted family of distributions and new models. J Probab Stat. 2016: 1-12.
Merovci F. Transmuted Rayleigh distribution. Aust J Stat. 2013; 42: 21-31.
Nikulin M, Haghighi F. A chi-squared test for the generalized power Weibull family for the head-and-neck cancer censored data. J Math Sci. 2006; 133: 1333-1341.
Nikulin M, Haghighi F. On the power generalized Weibull family: Model for cancer censored data, METRON. Int J Stat. 2009; 67: 75-86.
Olver FWJ, Lozier DM, Boisvert RF, Clark CW. NIST Handbook of Mathematical Functions. New York: Cambridge University Press; 2010.
R Core Team. R: A language and environment for statistical computing. Austria: the R Foundation for Statistical Computing; 2013.
Shaw W, Buckley I. The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. Proceeding of IMA Computational Finance Conference; 2007 March 23; London.
Smithson M, Verkuilen J. A better lemon-squeezer? Maximum likelihood regression with beta- distribuited dependent variables. Psycholog Meth. 2006; 11: 54-71.
Yuzhu T, Maozai T, Qianqian Zhu. Transmuted linear exponential distribution: A new generalization of the linear exponential distribution. Comm Stat Simulat Comput. 2014; 43: 2661-2677.
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Published
2018-07-19
How to Cite
Khan, M. S. (2018). Transmuted Generalized Power Weibull Distribution. Thailand Statistician, 16(2), 156–172. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/135560
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