Estimation of the survival function based on the log-logistic distribution

Document Type : Research Paper

Authors

Department of Mathematics, College of Education for pure Sciences, Ibn-Al-Haitham , University of Baghdad, Iraq

Abstract

This paper proposes a new method by hybrid Simplex Downhill Algorithm with Moment Method (SMOM) to estimate the parameters of Log-Logistic distribution based on Survival functions. Simulation is used to compare the suggested methods with two classical methods (Maximum Likelihood Estimator and with Moment Method). The results demonstrate that SMOM was efficient than the maximum likelihood Estimator and Moment method based on Mean Square Error (MSE).

Keywords

[1] K. A. Bayda, A new algorithm to estimate the parameters of log-logistic distribution based on the survival functions, J. Phys. Conf. Series, IOP Publishing, 1879 (2021) 032037.
[2] A. Cruz Joseph and S. Wishart David, Applications of machine learning in cancer prediction and prognosis, Cancer Inf. 2 (2006).
[3] K. Fotiadis Konstantina, P. Themis, P. Exarchos, P. Konstantinos, V. Michalis Karamouzis and I. Dimitrios, Machine learning applications in cancer prognosis and prediction, Comput. Struct. Biotech.J. 13 (2015) 8–17.
[4] C. Geerdens, P. Janssen and K. Van, Goodness-of-fit test for a parametric survival function with cure fraction, Test 29 (2020) 768–792.
[5] G. Kleinbaum David and M. Klein, Survival Analysis: A Self-learning Text, Springer Science & Business Media, 2006.
[6] J.A. Nelder and R. Mead, A simplex method for function minimization, Comput. J. 7 (1965) 308–313.
[7] M.O. Ojo and A.K. Olapade, On the generalized Logistic and Log-Logistic distribution, Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria, Kraguje vac J. Math. 25 (2003) 65–73.
[8] S. H. Raheem, H. K. Mansor, B. A. Kalaf and A. N. Salman, A Comparison for some of the estimation methods of the parallel stress-strength model In the case of inverse Rayleigh distribution, First Int. Conf. Comput. Appl. Sci. (2019) 22–27.
[9] R. Jason, N. John, P. Randal, V. Christof, N. Brian and W. Eric, A practical guide to understanding kaplan-meir curves, J. Amer. Acad. Otolary. Head Neck Surg. 143 (2010) 331–6.
[10] A.N. Salman, S.H. Rahiem and B.A. Kalaf,Estimate the scale parameter of exponential distribution via modified two stage shrinkage technique, J. College Educ. 2010(6) (2010) 62–75.
[11] R.P. Siarry Chelouah, A hybrid method combining continuous tabu search and neldermead simplex algorithms for the global optimization of multiminima functions, European J. Oper. Res. 161(3) (2005) 636–654.
[12] T.A.Y. AL-Yasseri, Using Simulation to Estimate Two Parameters and Reliability Function for Logistic Distribution, Master Thesis, College of Education, Al-Mustansirah University, 2014.
[13] A.A. Zaidan, B. Atiya, M.A. Bakar and B.B. Zaidan, A new hybrid algorithm of simulated annealing and simplex downhill for solving multiple-objective aggregate production planning on fuzzy environment, Neural Comput. Appl. 31 (2019) 1823–1834.
Volume 13, Issue 1
March 2022
Pages 127-141
  • Receive Date: 10 March 2021
  • Revise Date: 15 April 2021
  • Accept Date: 20 May 2021