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On the Exponentiated Generalized Modified Weibull Distribution

  • Aryal, Gokarna (Department of Mathematics, Computer Science, and Statistics, Purdue University Calumet) ;
  • Elbatal, Ibrahim (Institute of Statistical Studies and Research, Department of Mathematical Statistics, Cairo University)
  • Received : 2015.04.03
  • Accepted : 2015.07.08
  • Published : 2015.07.31

Abstract

In this paper, we study a generalization of the modified Weibull distribution. The generalization follows the recent work of Cordeiro et al. (2013) and is based on a class of exponentiated generalized distributions that can be interpreted as a double construction of Lehmann. We introduce a class of exponentiated generalized modified Weibull (EGMW) distribution and provide a list of some well-known distributions embedded within the proposed distribution. We derive some mathematical properties of this class that include ordinary moments, generating function and order statistics. We propose a maximum likelihood method to estimate model parameters and provide simulation results to assess the model performance. Real data is used to illustrate the usefulness of the proposed distribution for modeling reliability data.

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