The Beta Generalized Weibull distribution: Properties and applications

A five-parameter distribution called Beta Generalized Weibull (BGW) distribution is introduced. Beta Generalized Exponential (BGE), Beta Weibull (BW), Generalized or Exponentiated Weibull (GW or EW), Generalized Rayleigh (GR), Beta Exponential (BE), Generalized Exponential (GE), Weibull, Rayleigh and Exponential are its sub models. The cumulative distribution function (cdf) and the probability density function (pdf) have been expressed as mixtures of the Generalized Weibull cdfs and pdfs. The kth order moment has been derived. The non-linear equations for deriving the maximum likelihood estimators and the elements of the observed information matrix are presented. The distribution is found to be superior to the existing sub models on being fitted to two real data sets.

► A new five parameter distribution called Beta Generalized Weibull is introduced.
► It can accommodate all the four types of failure rate.
► It provides better results as compared to its sub models.
► It is flexible in modeling a wide spectrum of data sets in all areas of research.
► It is expected to have wider applications in reliability engineering.