Improved Likelihood Estimation for the Generalized Extreme Value and the Inverse Gaussian Lifetime Distributions

In presence of nuisance parameters, profile likelihood inference is often unreliable and biased, particularly in small sample scenario. Over past decades several adjustments have been proposed to modify profile likelihood function in literature including a modified profile likelihood estimation technique introduced in Barndorff--Nielsen. In this study, adjustment of profile likelihood function of parameter of interest in presence of nuisance parameter is investigated. We particularly focuss to extend the Barndorff--Nielsen's technique on Inverse Gaussian distribution for estimating its dispersion parameter and on generalized extreme value (GEV) distribution for estimating its shape parameter. The accelerated failure time models are used for lifetimes having GEV distribution and the Inverse Gaussian distribution is used for lifetime distribution. Monte-Carlo simulation studies are conducted to demonstrate the performances of both approaches. Simulation results suggest the superiority of the modified profile likelihood estimates over the profile likelihood estimates for the parameters of interest. Particularly, it is found that the modifications can improve the overall performance of the estimators through reducing their biases and standard errors.