On Generalized Linear Exponential Distribution: Different Methods of Estimation
Mahmoud, M., Ghazal, M., Radwan, H. (2020). On Generalized Linear Exponential Distribution: Different Methods of Estimation. EKB Journal Management System, 2(1), 8-13. doi: 10.21608/jmr.2019.15428.1007
M. A. W. Mahmoud; M. G. M. Ghazal; H. M. M. Radwan. "On Generalized Linear Exponential Distribution: Different Methods of Estimation". EKB Journal Management System, 2, 1, 2020, 8-13. doi: 10.21608/jmr.2019.15428.1007
Mahmoud, M., Ghazal, M., Radwan, H. (2020). 'On Generalized Linear Exponential Distribution: Different Methods of Estimation', EKB Journal Management System, 2(1), pp. 8-13. doi: 10.21608/jmr.2019.15428.1007
Mahmoud, M., Ghazal, M., Radwan, H. On Generalized Linear Exponential Distribution: Different Methods of Estimation. EKB Journal Management System, 2020; 2(1): 8-13. doi: 10.21608/jmr.2019.15428.1007

On Generalized Linear Exponential Distribution: Different Methods of Estimation

Journal of Modern Research
Article 2, Volume 2, Issue 1, January 2020, Page 8-13  XML PDF (771.08 K)
Document Type: Original Article
DOI: 10.21608/jmr.2019.15428.1007
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Authors
M. A. W. Mahmoudorcid 1; M. G. M. Ghazal2; H. M. M. Radwan email orcid 2
1Department of Mathematics, Faculty of Science, Al-Azhar University, 11884 Nasr city, Cairo, Egypt
2Department of Mathematics, Faculty of Science, Minia University, 61519 Minia, Egypt
Abstract
This paper concerns with various techniques for estimations from the generalized linear exponential distribution (GLED) that can be used for modeling bathtub, increasing and decreasing hazard rate (HR) behavior and was first proposed by [3]. This distribution is important since it contains as special sub-models some widely well-known distributions such as the exponential distribution (ED), the Rayleigh distribution (RD), the linear exponential distribution (LED), and the Weibull distribution (WD). The various techniques for estimations can be considered as maximum likelihood estimation (MLE), least-square estimation (LSE), weighted least square estimation (WLSE), Cramér Von-Mises estimation (CVME), and Anderson Darling estimation (ADE). These methods of estimations are used to estimate the unknown parameters of the well-known GLED. Two applications are used to show that the GLED is a viable distribution in modeling lifetime data and to compare the varying methods of estimations based on the Kolmogorov-Simnorov test with the corresponding P-value to show the optimal method. Finally, a simulation study is presented to compare the varying methods of estimation based on the mean square error (MSE) and the average absolute bias (AAB).
Keywords
Bathtub hazard rate; Increasing hazard rate; Least square and weighted least square estimations; Cramér Von-Mises estimation; Anderson Darling estimation
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