Approximation (M.S.E) of the shape parameter for Pareto distribution by using the standard Bayes estimator

Document Type : Research Paper

Authors

Institute of Medical Technology- Al-Mansour, Middle Technical University, Baghdad, Iraq

Abstract

In this paper, Pareto distribution was studied using a standard Bayes estimator. A Pareto distribution of two parameters is investigated to find the approximation of (M.S.E) of the shape parameter by depending on Tyler series of two variables to propose a model mathematically.

Keywords

[1] M.P. Alan, Introduction to statistical limit theory, 1st Edition, Chapman and Hall, 2011.
[2] B.C. Arnold, Pareto Distributions, Second Edition, CRC Press, Boca Raton, Florida, 2015.
[3] J. Chu, O. Dickin and S. Nadarajah, A review of goodness of fit test for Pareto distribution, J. Comput. Appl. Math. 36 (2019) 13–41.
[4] R. V. Hogg and S.A. Klugman, Loss Distribution, John Wiley and Sons New York, 1984.
[5] D.-H. Kim, Sang.-G. Kang and W.-D. Lee, Non-information prior for Pareto distribution, J. Korean Data Inf. Sci. Soc. 20 (2009) 1213–1223.
[6] A.A. Khaliq, Census of Life, Arabic Edition, Ammaan-Jordan, Dar Yazouri, 2011.
[7] E.L. Lehmann and G. Casella, Theory of Point Estimation, 2nd ed., John Wiley and Sons, NY., 2003.
[8] H. Levy and H.M. Markowitz, Approximating expected utility by a function of mean and variance, Amer. Econ. Rev. 69 (1979) 308–317.
[9] H.J. Malik, Estimation of the parameters of the Pareto distribution, Metrika Int. J. Theor. Appl.Stat. 15 (1970) 126–132.
[10] S. G. Meintanis and Y. Bassiakrs, Data-transformation and test of fit for the generalized Pareto hypothesis, Commun. Stat. Theory Methods 13 (2007) 1965–1979.
[11] A.M. Mood, F.A. Graybill and D.C. Boess, Introduction to The Theory of Statistics, Third Edition, McGraw-Hill, London, 1974.
[12] S. Nadarajah and S. Kotz, Reliability for Pareto Models, Metro Int. J. Stat. LXI(2) (2003) 191–204.
[13] L. Norman, J.K. Samuel and N. Balakrishnan, Continuous Univariate Distributions, Second Edition, Wiley, 1994.
[14] M. Obradovic, M. Jovanovic and B. Milosevie, Goodness-of-fit tests for Pareto distribution based on characterization and their asymptotics Statistics, J. Theor. Appl. Stat. 49 (2015) 1026–1041.
[15] W. Dong, D.-H. Kim and S.-G. Kang, Non-information prior for linear combinations of exponential means, J. Korean Data Inf. Sci. Soc. 27 (2016) 565–575.
Volume 13, Issue 1
March 2022
Pages 871-880
  • Receive Date: 04 August 2021
  • Accept Date: 17 September 2021