Journal of Statistics: Advances in Theory and ApplicationsAuthor's: N. Idowu Badmus and T. Adebayo Bamiduro
Pages: [91] - [107]
Received Date: March 25, 2014
Submitted by:
Two main distributions are combining by using the logit of beta function by Jones [10]. The weighted Weibull distribution proposed by Shahbaz et al. [19] and beta distribution in order to have a better distribution (beta-weighted Weibull distribution) than each of them individually in terms of the estimate of their characteristics in their parameters. We study and provide a comprehensive treatment of the mathematical properties of the beta weighted Weibull distribution and derive expressions for its moments and moment generating function, survival rate function, hazard rate function, skewness and kurtosis, coefficient of variation and asymptotic behaviours. We also discuss maximum likelihood estimation and provide formulae for the elements of the Fisher information matrix. The new distribution is apply to a lifetime data set and clearly shows that it is much more flexible and has a better representation of data than weighted Weibull distribution. We hope that this model may attract wider application in biology, biomedical, environmetric, and lifetime data analysis.
beta-weighted Weibull, Weibull, moment generating function, kurtosis, skewness.
