TY - JOUR

T1 - A Comparison of the Bayesian Method under Symmetric and Asymmetric Loss Functions to Estimate the Shape Parameter K of Burr Distribution

AU - Fithriani, I.

AU - Hakim, A. R.

AU - Novita, M.

N1 - Funding Information:
This work is supported by Hibah PITTA 2018 funded by DRPM Universitas Indonesia No.2308/UN2.R3.1/HKP.05.00/2018.
Publisher Copyright:
© Published under licence by IOP Publishing Ltd.

PY - 2018/12/4

Y1 - 2018/12/4

N2 - Burr distribution is one of the most important types of distribution in Burr system and has gained special attention. It has an important role in various disciplines, such as reliability analysis, life testing, survival analysis, actuarial science, economics, forestry, hydrology and meteorology. Thus, the parameter estimation for Burr distribution becomes an important thing to do. The frequentist approach using the maximum likelihood method is the most commonly used way to estimate the parameters of a distribution. In this paper we considered using the Bayesian method to estimate the shape parameter k of Burr distribution using gamma prior which is a conjugate prior. The Bayes estimate for the shape parameter k is obtained under the squared-error loss function (SELF) which is one of the symmetric loss function and the precautionary loss function (PLF) which is one of the asymmetric loss function. Through a simulation study, the comparison was made on the performance of the Bayes estimate for the shape parameter k under these two loss functions with respect to the mean-squared error (MSE) and the posterior risk.

AB - Burr distribution is one of the most important types of distribution in Burr system and has gained special attention. It has an important role in various disciplines, such as reliability analysis, life testing, survival analysis, actuarial science, economics, forestry, hydrology and meteorology. Thus, the parameter estimation for Burr distribution becomes an important thing to do. The frequentist approach using the maximum likelihood method is the most commonly used way to estimate the parameters of a distribution. In this paper we considered using the Bayesian method to estimate the shape parameter k of Burr distribution using gamma prior which is a conjugate prior. The Bayes estimate for the shape parameter k is obtained under the squared-error loss function (SELF) which is one of the symmetric loss function and the precautionary loss function (PLF) which is one of the asymmetric loss function. Through a simulation study, the comparison was made on the performance of the Bayes estimate for the shape parameter k under these two loss functions with respect to the mean-squared error (MSE) and the posterior risk.

UR - http://www.scopus.com/inward/record.url?scp=85058308230&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1108/1/012053

DO - 10.1088/1742-6596/1108/1/012053

M3 - Conference article

AN - SCOPUS:85058308230

VL - 1108

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012053

T2 - 2nd Mathematics, Informatics, Science and Education International Conference, MISEIC 2018

Y2 - 21 July 2018

ER -