A five-parameter distribution so-called the beta modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments and examine the order statistics and their moments. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.
Beta distribution Exponentiated exponential Exponentiated Weibull Generalized modified Weibull Maximum likelihood Modified Weibull Observed information matrix Weibull distribution
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Cox C, Chu H, Schneider MF, Mũoz A (2007) Tutorial in biostatistics: parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Stat Med 26: 4352–4374CrossRefMathSciNetGoogle Scholar
Kundu D, Rakab MZ (2005) Generalized Rayleigh distribution: different methods of estimation. Comput Stat Data Anal 49: 187–200zbMATHCrossRefGoogle Scholar
Lai CD, Xie M, Murthy DNP (2003) A modified Weibull distribution. Trans Reliab 52: 33–37CrossRefGoogle Scholar
Lee C, Famoye F, Olumolade O (2007) Beta-Weibull distribution: some properties and applications to censored data. J Mod Appl Stat Methods 6: 173–186Google Scholar
Mudholkar GS, Srivastava DK (1993) Exponentiated Weibull family for analyzing bathtub failure-real data. IEEE Trans Reliab 42: 299–302zbMATHCrossRefGoogle Scholar
Mudholkar GS, Srivastava DK, Friemer M (1995) The exponentiated Weibull family: a reanalysis of the bus-motor-failure data. Technometrics 37: 436–445zbMATHCrossRefGoogle Scholar
Mudholkar GS, Srivastava DK, Kollia GD (1996) A generalization of the Weibull distribution with application to the analysis of survival data. J Am Stat Assoc 91: 1575–1583zbMATHCrossRefMathSciNetGoogle Scholar