Bayesian inference for Pareto distribution with prior conjugate and prior non conjugate

Authors

  • Ferra YANUAR Andalas University
  • Cici Saputri Andalas University

DOI:

https://doi.org/10.20956/jmsk.v16i3.8019

Keywords:

Pareto distribution, posterior variance, absolute bias, Bayes confidence interval

Abstract

The purpose of this study is to determine the best estimator for estimating the shape   parameters of the Pareto distribution with the known  scale parameter. Estimation of these parameters is done by using the Gamma distribution as the prior distribution of the conjugate and the Uniform distribution as the non-conjugate prior distribution. A comparison of the two prior distributions is done through simulation studies with various sample sizes. The best estimator net is a method that produces the smallest posterior variance, absolute bias, and Bayes confidence interval. This study proves that the Bayes estimator by using the prior conjugate distribution produces all indicators of the goodness of the model with a smaller value than the non-conjugate prior distribution. Thus it can be concluded that the estimator with prior conjugate will produce a better predictive value than prior non-conjugate.

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References

Bain, Lee J. and M. Engelhardt.1992. Introduction to Probability and Mathematical Statistic Second Edition. Duxbury Press, California

Bolstad, W.M. 2007. Introduction to Bayesian Statistics Second Edition. A John Wiley & Sons, New York

Casella, G. and R.L. Berger. 2001. Statistical Inference Second Edition. Pasific Grove, California

Krishnamoorthy, K. 2006. Handbook of Statistical Distributions with Applications. Chapman & Hall/CRC

Mukhopadhyay, N. 2000. Probability and Statistical Inference. Marcel Dekker, New York

Walpole, E.R. 1986. Pengantar Statitika Edisi Ketiga. PT Gramedia Pustaka Utama : Jakarta

Walpole, E.R. dan Myers, R.H. 1995. Ilmu Peluang dan Statistika untuk Insinyur & Ilmuwan Edisi Keempat. ITB : Bandung

Yanuar, F., H. Yozza dan R.V. Rescha. 2019. Comparison of Two Priors in Bayesian Estimation for Parameter of Weibull Distribution. Science and Technology Indonesia. 4(3): 82 - 87

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Published

2020-04-28

Issue

Section

Research Articles