A New Rayleigh Distribution: Properties and Estimation Based on Progressive Type-II Censored Data with an Application

In this paper, we propose a new extension of the traditional Rayleigh distribution called the modified Kies Rayleigh distribution. The new distribution contains one scale and one shape parameter and its hazard rate function can be increasing and bathtub-shaped. Some mathematical properties of the new distribution are derived including quantiles and moments. The parameters of modified Kies Rayleigh distribution are estimated based on progressively Type-II censored data. For this purpose, we consider two estimation methods, namely maximum likelihood and maximum product of spacing estimation methods. To compare the efficiency of the proposed estimators, a simulation study is carried out. To show the applicability of the new model as well as the estimation methods, one real data for failure times of software is analyzed. Based on the empirical parts, we can conclude that the proposed model can be considered as a good model in the field of life testing and reliability analysis compared with other competing models.