Bayesian Estimation of a Transmuted Topp-Leone Length Biased Exponential Model Based on Competing Risk with the Application of Electrical Appliances

Abstract

Competing risk (CoR) models are frequently disregarded in failure rate analysis, and traditional statistical approaches are used to study the event of interest. In this paper, we proposed a new lifetime distribution by generalizing the length biased exponential (LBE) distribution using the transmuted Topp-Leone-G (TTL-G) family of distributions. The new three parameter model is called the transmuted Topp-Leone length biased exponential (TTLLBE) distribution. A comprehensive account of various mathematical features of the TTLLBE model are derived. The unknown parameters of the proposed distribution are estimated by six classical approaches: the maximum likelihood (ML) approach, maximum product spacing (MPS) approach, least square (LS) approach, Weighted LS (WLS) approach, Cramér-Von Mises (CVN) approach, Anderson–Darling (AD) approach, and Bayesian approach. The stability of the model parameters is examined through the simulation study. The applications of our proposed distribution are explained through real data and its performance is illustrated through its comparison with the competent existing distributions. The TTLLBE model depend on the CoR model has been obtained and estimated parameter of this model by ML and Bayesian estimation approaches. In electrical appliances, we found two main causes of failure, and the data of electrical appliances are fitted to our model. Therefore, we analyzed the TTLLBE model depend on the CoR model to obtain the strong cause of failure.