Bayesian and non-Bayesian estimations for a flexible reduced logarithmic-inverse Lomax distribution under progressive hybrid type-Ⅰ censored data with a head and neck cancer application

This article used classical and Bayesian procedures to discuss the statistical inferences to the unknown parameters of the flexible reduced logarithmic-inverse Lomax distribution based on a progressive hybrid type-Ⅰ censoring (PHT-ICS) approach. The maximum likelihood and Bayesian estimation techniques estimate unknown parameters, reliability, and hazard rate functions. The investigation of Bayes estimators makes use of the gamma priors and symmetric and asymmetric loss functions. Additionally, the classical asymptotic confidence intervals and the credible intervals were explored. A simulation study and a bladder cancer application are presented to illustrate the proposed estimation methods. The flexible reduced logarithmic-inverse Lomax (FRL-IL) distribution's relevance and the given estimators' effectiveness were evaluated using failure data from a sample of 44 patients diagnosed with head and neck cancer. The results show that likelihood based on the Markov chain Monte Carlo (MCMC) method has the smallest mean squared error (MSE) values. In contrast, Bayes estimators with the assumed informative prior outperformed maximum likelihood estimators and Bayes estimators under the squared error loss function in terms of MSEs.