Power Generalized Weibull Distribution Based on Record Values and Associated Inferences with Bladder Cancer Data Example

Abstract

The power generalized Weibull distribution has been proposed recently by [24] as an alternative to the gamma, Weibull and the exponentiated Weibull distributions. The power generalized Weibull family is suitable for modeling data that indicate nonmonotone hazard rates and can be used in survival analysis and reliability studies. Usefulness and flexibility of the family are illustrated by reanalyzing Efron’s data pertaining to a head-and-neck cancer clinical trial. These data involve censoring and indicate unimodal hazard rate. For this distribution, some recurrence relations are established for the single and product moments of upper record values. Further, using these relations, we have obtained means, variances and covariances of upper record values from samples of sizes up to 10 for various values of the parameters and present them in figures. Real data set is analyzed to illustrate the flexibility and importance of the model.

Keywords

Record values / Moments / Characterization / Power generalized Weibull distribution