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

Rania A. H. Mohamed, Ibrahim Elbatal, Ehab M. ALmetwally, Mohammed Elgarhy and Hisham M. Almongy ()
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Rania A. H. Mohamed: Department of Statistics, Mathematics and Insurance, Faculty of Commerce, Port Said University, Port Fouad 42526, Egypt
Ibrahim Elbatal: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia
Ehab M. ALmetwally: Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
Mohammed Elgarhy: The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra 31951, Egypt
Hisham M. Almongy: Department of Applied Statistics and Insurance, Faculty of Commerce, Mansoura University, El-Mansoura 35516, Egypt

Mathematics, 2022, vol. 10, issue 21, 1-23

Abstract: Competing risk ( C o R ) 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 ( T T L - G ) family of distributions. The new three parameter model is called the transmuted Topp-Leone length biased exponential ( T T L L B E ) distribution. A comprehensive account of various mathematical features of the T T L L B E 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 T T L L B E model depend on the C o R 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 T T L L B E model depend on the C o R model to obtain the strong cause of failure.

Keywords: competing risk model; transmuted Topp-Leone family; Bayesian analysis; simulation; entropy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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