Bayesian Generalized Self Method to Estimate Scale Parameter of Invers Rayleigh Distribution
Abstract
The purposes of this study are to estimate the scale parameter of Invers Rayleigh distribution under MLE and Bayesian Generalized square error loss function (SELF). The posterior distribution is considered to use two types of prior, namely Jeffrey’s prior and exponential distribution. The proposed methods are then employed in the real data. Several criteria for the selection model are considered in order to identify the method which results in a suitable value of parameter estimated. This study found that Bayesian Generalized SELF under Jeffrey’s prior yielded better estimation values that MLE and Bayesian Generalized SELF under exponential distribution.
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Rasheed, A. (2016) Reliability Estimation in Inverse Rayleigh Distribution using Precautionary Loss Function. Mathematics and Statistics Journal, 2, 9–15.
Soliman, A.A. and Al-Aboud, F.M. (2008) Bayesian inference using record values from Rayleigh model with application. European Journal of Operational Research, 185, 659–72. https://doi.org/10.1016/j.ejor.2007.01.023
Aslam, M. and Jun, C.-H. (2009) A Group Acceptance Sampling Plans For Truncated Life Tests Based On The Inverse Rayleigh And Log-Logistic Distributions. Pakistan Journal of Statistics, 25, 107–19.
Soliman, A., Amin, E.A. and Aziz, A.A.A.-E. (2010) Estimation and Prediction from Inverse Rayleigh Distribution Based on Lower Record Values. Applied Mathematical Sciences, 4, 3057–66.
Ali, S. (2015) Mixture of the inverse Rayleigh distribution: Properties and estimation in a Bayesian framework. Applied Mathematical Modelling, 39, 515–30. https://doi.org/10.1016/j.apm.2014.05.039
Dey, S. and Dey, T. (2011) Bayesian Estimation and Prediction on Inverse Rayleigh Distribution. International Journal of Information and Management Sciences, 22, 1–15.
Yousef, A.H. and Lafta, A. (2012) Comparison Between Methods of The Scale Parameter. FES: Finance, Economy, Strategy, 58, 22–30.
Dey, S. (2012) Bayesian Estimation and Prediction on Inverse Rayleigh Distribution. Malaysian Journal of Mathematical Sciences, 6, 113–24.
Rasheed, H.A. (2017) Comparison of Bayes Estimators for Parameter and Relia-bility Function for Inverse Rayleigh Distribution by Using Generalized Square Error Loss Function. Al-Mustansiriyah Journal of Science, 28, 162–8. https://doi.org/10.23851/mjs.v28i2.512
Yanuar, F. (2016) The Health Status Model in Urban and Rural Society in West Sumatera, Indonesia: An Approach of Structural Equation Modeling. Indian Journal of Science and Technology, 9, 8.
Yanuar, F., Ibrahim, K. and Jemain, A.A. (2013) Bayesian structural equation modeling for the health index. Journal of Applied Statistics, 40, 1254–69. https://doi.org/10.1080/02664763.2013.785491
Yanuar, F., Yozza, H. and Rescha, R.V. (2019) Comparison of Two Priors in Bayesian Estimation for Parameter of Weibull Distribution. Science and Technology Indonesia, 4, 82. https://doi.org/10.26554/sti.2019.4.3.82-87
Burnham, K.P. and Anderson, D.R. (2002) Model selection and multimodel inference: a practical information-theoretic approach. 2. ed., [4. printing]. Springer, New York, NY.
Fatima, K. and Ahmad, S.P. (2017) Weighted Inverse Rayleigh Distribution. International Journal of Statistics and Systems, 12, 119–37.
DOI: https://doi.org/10.18860/ca.v6i4.11482
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