Modeling and analysis of lifetime data is an important aspect of statistical work in a wide variety of applications. However, the data in many applications such as economics, engineering, biological studies, environmental sciences, medical sciences and finance can be considered as data coming from a mixture population of two or more different distributions. Mixture classical distributions have a limited ability to represent real data. A new mixture model called Weibull Rayleigh mixture model is introduced in this paper. The proposed model is based on components of the composite Weibull Rayleigh distribution. The interest of this model is that the density function can take different possible shapes, symmetric and asymmetric. Moreover, the behaviour of the related hazard function varies and can increase or decrease. The new model turns out to be quite flexible for modeling positive data. The maximum likelihood estimation method is applied to obtain the estimators of the parameters of the new model based on Type-I, Type-II censored samples and complete samples. The statistical characteristics of this distribution are obtained such as moment, incomplete moment, order statistic and others. A Monte Carlo simulation study is employed to check the consistency of the estimates of model parameters using different sample sizes. The model's performance is evaluated by comparing it to other competing distributions using three sets of real data. The proposed model is superior to its counterparts' models in representing the different data sets.

Weibull Rayleigh distribution, maximum likelihood estimation bias, means squared error, Type-I censored samples, Type-II censored samples.