The Exponentiated Generalized Class of Distributions

Abstract: We propose a new method of adding two parameters to a continuous distribution that extends the idea first introduced by Lehmann (1953) and studied by Nadarajah and Kotz (2006). This method leads to a new class of exponentiated generalized distributions that can be interpreted as a double construction of Lehmann alternatives. Some special models are discussed. We derive some mathematical properties of this class including the ordinary moments, generating function, mean deviations and order statistics. Maximum likelihood estimation is investigated and four applications to real data are presented.

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

[2]  Harold Exton,et al.  Handbook of Hypergeometric Integrals: Theory, Applications, Tables, Computer Programs , 1978 .

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

[4]  Pushpa L. Gupta,et al.  Modeling failure time data by lehman alternatives , 1998 .

[5]  D. Kundu,et al.  EXPONENTIATED EXPONENTIAL FAMILY: AN ALTERNATIVE TO GAMMA AND WEIBULL DISTRIBUTIONS , 2001 .

[6]  D. Kundu,et al.  Theory & Methods: Generalized exponential distributions , 1999 .

[7]  Malwane M. A. Ananda,et al.  A Generalization of the Half-Normal Distribution with Applications to Lifetime Data , 2008 .

[8]  Erich L. Lehmann,et al.  The Power of Rank Tests , 1953 .

[9]  Samuel Kotz,et al.  The Exponentiated Type Distributions , 2006 .

[10]  F. Famoye,et al.  BETA-NORMAL DISTRIBUTION AND ITS APPLICATIONS , 2002 .

[11]  Saralees Nadarajah,et al.  The Exponentiated Gamma Distribution with Application to Drought Data , 2007 .

[12]  F. Famoye,et al.  The beta-Pareto distribution , 2008 .

[13]  Saralees Nadarajah,et al.  The exponentiated Gumbel distribution with climate application , 2006 .

[14]  G. S. Mudholkar,et al.  A Generalization of the Weibull Distribution with Application to the Analysis of Survival Data , 1996 .

[15]  M. Spoto,et al.  POSTHARVEST MODIFICATIONS OF MECHANICALLY INJURED BANANAS. , 2010 .

[16]  Yu. A. Brychkov,et al.  Integrals and series , 1992 .

[17]  M. A. Chaudhry,et al.  On a Class of Incomplete Gamma Functions with Applications , 2001 .

[18]  Saralees Nadarajah,et al.  Closed-form expressions for moments of a class of beta generalized distributions , 2011 .