Parameter Estimation of Beta-Exponential Distribution Using Linear Combination of Order Statistics

Abstract

Beta-Exponential Distribution (BED) is proposed by Nadarajah and Samuel Kotz which contains several well-known distributions. With the addition of two shape parameters, this distribution can fit a wider range of data and therefore has been widely used in life testing. However, there are few literature on the properties of order statitics from this distribution, especially the best linear unbiased estimation (BLUE) of the location-scale parameters. In this paper, a new algorithm is proposed by us to obtain closed-form expression for variance-covariance matrix of order statistics from this distribution and give the BLUE for the location-scale parameters for the first time. Compared with several other classical parameter estimation methods (MLE, trimmed L-moments (TL-moments), probability weighted moments (PWM)), BLUE is more suitable for location-scale parameter estimation under small sample size for this distribution. Besides, the explicit expressions for moments of order statistics under the independent identically distributed (IID) case and independent not identically distributed (INID) case are also derived. Furthermore, for BED with three parameters (two shape parameters and scale parameter), we propose an improved TL-moments estimation method based on order statistics isotone transformation under two different trimmed schemes (

s=t=1

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and

s=1,t=0

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) as well as an improved PWM estimation method and conduct simulation study to compare the performance of each new method with MLE. As a result, the improved TL-moments estimation (

s=t=1

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) and the improved PWM estimation perform better than MLE on the whole.

Keywords

Beta-exponential distribution / Order statistics / Improved TL-moments / Improved PWM / BLUE

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Funding

ScienceandTechnologyProgramofBeijingEducationCommission(No.KM202110005013)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature