A modified maximum likelihood estimation for the three parameters in lognormal distribution model / Faiz Zulkifli, Noorizam Daud and Norazan Mohamed Ramli

The introduction of the threshold parameters in three parameters lognormal distribution(λ ,μ ,σ) creates complications when we seek to estimate these parameters from sample. Hill(1963) has shown that global maximum likelihood estimators resulted in inadmissibleestimates as the likelihood function of any ordered sample tends to infinity when(λ ,μ ,σ ) approach( ,−∞, ∞) 1 x respectively. Hence, in this project we would like to propose anew modified version of maximum likelihood estimation to cater for the above problem. Theperformance of the proposed method compared to the existing method suggested by Cohenand Whitten (1980), will be examined and verified through a rigorous simulation procedureusing S-PLUS programming language. A sensitivity analysis will be conducted to study thebehaviour of the estimators in meeting the asymptotic normality assumption. For illustration,the proposed method will be applied to real data sets such as biological and physical sciencesdata.