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A New Three-Parameter Exponential Distribution with Variable Shapes for the Hazard Rate: Estimation and Applications

Ahmed Z. Afify () and Osama Abdo Mohamed ()
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Ahmed Z. Afify: Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt
Osama Abdo Mohamed: Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44511, Egypt

Mathematics, 2020, vol. 8, issue 1, 1-17

Abstract: In this paper, we study a new flexible three-parameter exponential distribution called the extended odd Weibull exponential distribution, which can have constant, decreasing, increasing, bathtub, upside-down bathtub and reversed-J shaped hazard rates, and right-skewed, left-skewed, symmetrical, and reversed-J shaped densities. Some mathematical properties of the proposed distribution are derived. The model parameters are estimated via eight frequentist estimation methods called, the maximum likelihood estimators, least squares and weighted least-squares estimators, maximum product of spacing estimators, Cramér-von Mises estimators, percentiles estimators, and Anderson-Darling and right-tail Anderson-Darling estimators. Extensive simulations are conducted to compare the performance of these estimation methods for small and large samples. Four practical data sets from the fields of medicine, engineering, and reliability are analyzed, proving the usefulness and flexibility of the proposed distribution.

Keywords: Anderson-Darling estimation; Cramér-von Mises estimation; data analysis; exponential distribution; mean residual life; percentiles estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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