Bayesian and Non-Bayesian Inference for the Trigonometric Extended Rayleigh-Weibull Model Under Progressively Censored Data

In this paper, a new extension of the Rayleigh-Weibull (RW) model, called the sine Rayleigh-Weibull (SRW) model, is proposed. This model is constructed using the trigonometrically generated family of distributions based on sine functions and involves two parameters. The SRW model provides greater flexibility than the RW model and several other well-known statistical models, such as the sine-Weibull, exponential, Weibull, and Rayleigh distributions. Its hazard rate function can exhibit various shapes, including constant, J-shaped, or increasing forms. Under a progressive Type-II censoring scheme, statistical inference for the parameters of the SRW model is a central focus of this study. To estimate the parameters, we employ various methods, including the Expectation-Maximization (EM) algorithm. Under the Bayesian framework, parameter estimation is conducted using Markov Chain Monte Carlo (MCMC) methods and the Tierney-Kadane approximation, with respect to different loss functions, such as the squared error loss and the linear exponential loss. The numerical properties of the proposed estimators are assessed through Monte Carlo simulations, and the model is further validated by application to real datasets from the fields of electrical appliances and survival times of breast cancer patients.