Bias reduction of maximum likelihood estimation in exponentiated Teissier distribution

The exponentiated Teissier distribution (ETD) offers an alternative for modeling survival data, taking into account flexibility in modeling data with increasing and decreasing hazard rate functions. The most popular method for parameter estimation of the ETD distribution is the maximum likelihood estimation (MLE). The MLE, on the other hand, is notoriously biased for its small sample sizes. We are therefore driven to generate virtually unbiased estimators for ETD parameters. More specifically, we focus on two methods of bias correction, bootstrapping and analytical approaches, to reduce MLE biases to the second order of bias. The performances of these approaches are compared through Monte Carlo simulations and two real-data applications.