The Extended Alpha Power Transformed Family of Distributions: Properties and Applications

Zubair Ahmad ； Muhammad Ilyas ； G. G. Hamedani

《Journal of Data Science》 17卷4期 (2019/10) Pp. 726-741

https://doi.org/10.6339/JDS.201910_17(4).0006

摘要

In this article, a new family of lifetime distributions by adding an additional parameter to the existing distributions is introduced. The new family is called, the extended alpha power transformed family of distributions. For the proposed family, explicit expressions for some mathematical properties along with estimation of parameters through Maximum likelihood Method are discussed. A special sub-model, called the extended alpha power transformed Weibull distribution is considered in detail. The proposed model is very flexible and can be used to model data with increasing, decreasing or bathtub shaped hazard rates. To access the behavior of the model parameters, a small simulation study has also been carried out. For the new family, some useful characterizations are also presented. Finally, the potentiality of the proposed method is showen via analyzing two real data sets taken from reliability engineering and bio-medical fields.

關鍵字

Family of distributions ； Alpha power transformation ； Weibull distribution ； Moments ； Order statistic ； Residual life function ； Maximum likelihood estimation