  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.
