Modified Profile Likelihood Estimation in the Lomax Distribution

In this paper, we consider improving maximum likelihood inference for the scale parameter of Lomax distribution. The improvement is based on using modifications to estimator Barndorff-Nielsen modification profile function. We apply these obtain improved estimators distribution in presence a nuisance shape parameter. Due complicated expression Barndorff-Nielsen's modification, several approximations are considered including empirical covariances and approximation suitably derived approximate ancillary statistics. obtained function corresponding modified estimators. They not available simple closed forms can be numerically as roots some equations. Comparisons between terms their biases mean squared errors were carried out simulation techniques. found that have best performance according criteria used. Therefore recommend use version parameter, especially small sample sizes with heavy censoring, which quite common industrial life testing experiments reliability studies. An example real data given illustrate methods paper.