On Generalized Linear Exponential Distribution: Different Methods of Estimation

Mahmoud, M. A. W.; Ghazal, M. G. M.; Radwan, H. M. M.

doi:10.21608/jmr.2019.15428.1007

On Generalized Linear Exponential Distribution: Different Methods of Estimation

Document Type : Original Article

Authors

¹ Department of Mathematics, Faculty of Science, Al-Azhar University, 11884 Nasr city, Cairo, Egypt

² Department of Mathematics, Faculty of Science, Minia University, 61519 Minia, Egypt

10.21608/jmr.2019.15428.1007

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).

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