Bias Reduction of Maximum Likelihood Estimation in the Unit Odd Lindley Half-Logistic Model with Applications to Medicine and Geology Real Datasets

In this study, the exponential transformation method is used to introduce the unit odd Lindley half-logistic (UOLHL), a bounded form of the odd Lindley half-logistic distribution. The new model can handle increasing-bathtub-shaped and increasing hazard rate functions, making it appropriate for modeling unit interval data. Additional propositions on moments and conditional moments round up the theoretical part. Different estimation methods are used to determine our proposed model estimator. In addition, the maximum likelihood approach is used to justify the estimation of the UOLHL parameter, and the approach used for this model produced a biased estimate for small sample sizes. As a result, our objective here is to reduce both the bias and root mean square error of the maximum likelihood estimate (MLE) of the UOLHL parameter. In this regard, we concentrate on three techniques for bias correction of MLEs of the proposed model’s parameter. The Cox-Snell technique is the first approach, followed by the parametric bootstrapping method in the second and the Firth method in the third. The performance of the regular biases and three earlier approaches is compared using Monte Carlo simulations. The results we achieve show that bias adjustments improve estimate accuracy. Finally, a medicine real dataset was used to show the superiority of our proposed model for fitting this dataset compared with other models. Also, two real geology datasets were analyzed to illustrate the importance of the proposed model bias-corrected estimators.