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Bayesian Methods and Maximum Likelihood Estimations of Exponential Censored Time Distribution with Cure Fraction

Dr. Al Omari Mohammed Ahmed
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Dr. Al Omari Mohammed Ahmed: Department of Mathematics, Faculty of Arts and Science in Qilwah, AlBaha University, Baha, Saudi Arabia

Academic Journal of Applied Mathematical Sciences, 2021, vol. 7, issue 2, 106-112

Abstract: This paper is focused on estimating the parameter of Exponential distribution under right-censored data with cure fraction. The maximum likelihood estimation and Bayesian approach were used. The Bayesian method is implemented using gamma, Jeffreys, and extension of Jeffreys priors with two loss functions, which are; squared error loss function and Linear Exponential Loss Function (LINEX). The methods of the Bayesian approach are compared to maximum likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) to determine the best for estimating the parameter of Exponential distribution under right-censored data with cure fraction. The results show that the Bayesian with gamma prior under LINEX loss function is a better estimation of the parameter of Exponential distribution with cure fraction based on right-censored data.

Keywords: Exponential distribution; Maximum likelihood estimation; Bayesian method; Right censored data; Cure fraction. (search for similar items in EconPapers)
Date: 2021
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