International Journal of Nonlinear Analysis and Applications

Estimation of parameter for the Pareto distribution based on right censoring

Document Type : Research Paper

Authors

1 Department of pharmacognosy and medicinal plants, University of Basrah, Iraq

2 Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq

Abstract

In this paper, we found the estimation of the unknown parameter $\delta$ when $\vartheta$  is a known parameter in the Pareto distribution. First, we get the maximum probability estimators(MLEs) for unknown parameters. We have obtained the Bayes Estimators of unknown parameter $\delta$  using Lindley's approximation. A Monte Carlo simulation is performed and used a programming language R to compare the performance of the method used, and the data set was analyzed for illustration purposes.

Keywords

[1] B.C. Arnold and S.J. Press, Bayesian estimation and prediction for pareto data, J. Amer. Stat. Assoc. 84(408)
(1989) 1079–1084.
[2] L. Briliano, S. Abdullah and I. Fithriani, Parameter estimation of burr distribution for right censored data with
bayes method, AIP Conf. Proc. 2242 (2020) 030004.
[3] J. Cahoon and R. Martin, Generalized inferential models for censored data, Int. J. Appr. Reas. 137 (2021) 51–66.
[4] S. Datta, Estimating the mean life time using right censored data, Stat. Method. 2(1) (2005) 65–69.
[5] F. Ducros and P. Pamphile, Bayesian estimation of weibull mixture in heavily censored data setting, Reliability
Engin. Syst. Safety, 180 (2018) 453–462.
[6] W.K. Ghafil, T. J. Khraibet and A.A. Alwan, Maximum likelihood and bayesian estimation of rayleigh with partly
interval-censored case-i data, Neuro Quantol. 18(5) (2020) 26–28.
[7] W.K. Ghafil and R.H. Shamkhi, Parametric regression analysis of bivariate the proportional hazards model with
current status data, Int. J. Nonlinear Anal. Appl. 12(2)(2021) 1591–1598.
[8] J.H. Kim, S. Ahn and S. Ahn, Parameter estimation of the pareto distribution using a pivotal quantity, J. Korean
Stat. Soc. 46(3) (2017) 438–450.
[9] N. Kim, On the maximum likelihood estimation for a normal distribution under random censoring, Commun.
Stat. Appl. Meth. 25(6) (2018) 647–658.
[10] A. Lavanya and T.L. Alexander, Estimation of parameters using lindley’s method, Int. J. Adv. Res. 4(12) (2016)
1767–1778.
[11] R.E. Quandt, Old and mew methods op estimation and the pareto distribution, Metrika 10 (1964) 55-–82.
[12] A. Rasheed and A. Al-Gazi, Bayes estimators for the shape parameter of pareto type ii distribution under generalized square error loss function, Math. Theory Model. 6(11) (2014) 20–32.
[13] M. Rytgaard, Estimation in the pareto distribution, ASTIN Bulletin: The Journal of the IAA 20(2) (1990)
201–216.
[14] J.I. Seo, S.B. Kang and H.Y. Kim, New approach for analysis of progressive type-II censored data from the pareto
distribution, Commun. Stat. Appl. Meth. 25(5)(2018) 569–575.
[15] R. Shinohara, Estimation of Survival of Left Truncated and Right Censored Data Under Increasing Hazard, Master
of Science, Mc Gill University, Montreal, Quebec, 2007.
[16] K.S. Sultan and W. Emam, The combined-unified hybrid censored samples from pareto distribution: Estimation
and properties, Appl. Sci. 11(13) (2021) 6000.
[17] X. Wang and W. Gui, Bayesian estimation of entropy for burr type xii distribution under progressive type-ii
censored data, Math. 9(4)(2021) 313.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 1873-1877
  • Receive Date: 16 May 2021
  • Revise Date: 05 September 2021
  • Accept Date: 20 September 2021
  • First Publish Date: 16 November 2021