International Journal of Nonlinear Analysis and Applications

Estimating the survival and risk functions of a log-logistic distribution by using order statistics with practical application

Document Type : Research Paper

Authors

College of Administration and Economics, Department of Statistics, University of Baghdad, Iraq

Abstract

The Log-Logistic distribution is one of the important statistical distributions as it can be applied in many fields (biological, chemical and physical experiments) and its importance comes from the importance of determining the survival and risk function for these experiments. The research will work to determine the characteristics of the distribution through the use of order statistics to estimate its parameters using the approved standard Bayes method On the squared loss function (Bayslf) and determining the optimal method by comparing it with the MLE method according to a simulation method by taking different models for default values for parameter and different sample sizes and with MSE, IMSE comparison criteria as well as applying it to real data for breast cancer patients and  determine survival and risk function

Keywords

[1] E. G. AbdelQader, Estimating the parameters of the Lomax distribution using generalized order statistics, Master’s thesis in statistics submitted to the College of Computer Science and Mathematics at the University of Mosul, 2018.
[2] M. A. Alrubeyi, Nonparametric and semi-parametric Bayesian estimations for right-censored survival data of the using the Gibbs sampler with practical application, Master’s thesis in Statistics submitted to the College of Administration and Economics at the University of Baghdad, 2019.
[3] B. F. Al-Saadi, Some parametric and non-parametric methods for estimating the reliability function with practical application, Master’s thesis in Statistics submitted to the College of Administration and Economics at the University of Baghdad, (2010).
[4] D Chen, X Chen, J Wang, Z Zhang, Y Wang, C. Jia and X. Hu, Estimation of thermal time model parameters for seed germination in 15 species: the importance of distribution function, Seed Sci. Res. , 31 ( 2 )(2021) 83 - 90, https://doi.org/10.1017/S0960258521000040.
[5] A. Dixit, Exact Comparison of Hazard Rate Functions of Log-Logistic Survival Distributions, A Thesis Submitted to the Graduate Faculty of Auburn University, 2008.
[6] R.B. Hooge and A. T. Craig, Introduction to mathematical statistics, 3rded, The Macmillan Company, New York, 1966.
[7] H. A. Howladera and G. Weissb, Log-logistic survival estimation based on failure-censored data, J. Appl. Stat., 2(19)(1992) 231- 240.
[8] U. Kamps, A concept of generalized order statistics, J. Stat. Plann. Inference, 48(1995) 1-23.
[9] D.V. Lindley, Approximate Bayesian Methods, Trabajos de Estadistica Y de Investigacion Operativa, 31(1980) 223–245, https://doi.org/10.1007/BF02888353.
[10] A. Ragab and J. Green, On order statistics from the log-logistic distribution and their properties, Commun. Stat.- Theory Methods, 13(21)(1984) 2713-2724.
[11] A. A. Saleh, Methods for estimating the risk function for the Quasi-Lindely distribution, comparative research with practical application, Master’s thesis in Statistics submitted to the College of Administration and Economics at the University of Baghdad, 2016.
[12] V. P. Singh and H. Guo, Parameter Estimation For 2-parameter Log-logistic Distribution by Maximum Entropy, Civ. Eng. Syst., 12(2005) 343-357.
[13] A. E. A. Teamah, A. A. Elbanna and A. M. Gemeay, Heavy-Tailed Log-Logistic Distribution: Properties, Risk Measures and Applications, Optim. Inf. Comput., (2021), https://doi.org/10.19139/soic-2310-5070-1220.
[14] A. H. Yousef Al-Saray, S. H. A. Al-Jasim, Statistical Decision Theory and Its Applications, Al-Jazeera Office for Printing and Publishing - Baghdad, 2012.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 2483-2502
  • Receive Date: 15 June 2021
  • Accept Date: 11 November 2021