Bias Reduction of Maximum Likelihood Estimation in the Inverse Xgamma Distribution

A distribution for modeling survival data that accounts for flexibility in modeling data with upside-down bathtub-shaped hazard rate functions is the inverse Xgamma distribution (IXG). The maximum likelihood method (MLE) is the most often used technique for parameter estimation of the IXG distribution. Conversely, the MLE is infamously biased for small sample sizes. This motivates us to produce almost unbiased estimators for IXG parameter. More precisely, we minimize MLE biases to the second degree of bias using two techniques for bias correction: bootstrap and analytical approaches. Two actual data applications and Monte Carlo simulations are used to compare the performances of these methods.