Next Article in Journal
On the Fractional Order Rodrigues Formula for the Shifted Legendre-Type Matrix Polynomials
Previous Article in Journal
Parameter and State Estimation of One-Dimensional Infiltration Processes: A Simultaneous Approach
Open AccessArticle

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

1
Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt
2
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44511, Egypt
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 135; https://doi.org/10.3390/math8010135
Received: 4 December 2019 / Revised: 12 January 2020 / Accepted: 13 January 2020 / Published: 16 January 2020
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. View Full-Text
Keywords: Anderson-Darling estimation; Cramér-von Mises estimation; data analysis; exponential distribution; mean residual life; percentiles estimation Anderson-Darling estimation; Cramér-von Mises estimation; data analysis; exponential distribution; mean residual life; percentiles estimation
Show Figures

Figure 1

MDPI and ACS Style

Afify, A.Z.; Mohamed, O.A. A New Three-Parameter Exponential Distribution with Variable Shapes for the Hazard Rate: Estimation and Applications. Mathematics 2020, 8, 135.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop