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Estimation for a half-triangular distribution based on uni ed hybrid censored sample
Journal of the Korean Data & Information Science Society 2018;29:1697-706
Published online November 30, 2018
© 2018 Korean Data and Information Science Society.

Young Eun Jeon1 · Suk-Bok Kang2

12Department of Statistics, Yeungnam University
Correspondence to: Professor, Department of Statistics, Yeungnam University, Gyeongsan 38541, Korea. E-mail: sbkang@yu.ac.kr
Received October 29, 2018; Revised November 18, 2018; Accepted November 19, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper, we derive some estimators of the scale parameter of half-triangular distribution based on uni ed hybrid censored samples. First, we obtain the maximum likelihood estimator (MLE) of the scale parameter. However, the MLE can't be obtained explicitly with closed form because of the nonlinearity of the likelihood equation. So, we propose some approximate maximum likelihood estimators (AMLEs) using two di erent types of Taylor series expansions for some nonlinear functions of the likelihood equation. Finally, we compare the proposed estimators in the sense of the mean squared error (MSE) through Monte Carlo simulation. From the simulation results, we can show that the proposed AMLEs are usually more ecient than the MLE.
Keywords : Approximate maximum likelihood estimator, half-triangular distribution, maximum likelihood estimator, uni ed hybrid censoring