Advancing estimation techniques and their applications in engineering and medical data analysis through novel continuous and discrete linear failure rate distribution extension

In this paper, we present a new heavy-tailed distribution called the heavy-tailed linear failure rate (HTLFR) distribution. Various statistical properties of the proposed distribution are derived, including the quantile function, the median, the ordinary moments, the moment generating function, the incomplete moments and the conditional moments. Some actuarial measures such as value at risk, expected shortfall, tail value at risk, tail variance and tail variance premium are calculated. Three different methods of estimation such as the maximum likelihood method, the maximum product spacing method and the Bayesian method as well as some simulation results for the model parameters of the HTLFR distribution under complete samples are examined. The results of the real data set show that the proposed distribution has greater flexibility and has been empirically evaluated under complete data. Discrimination analysis was employed to ensure fairness, equity, and accuracy in decision-making processes for selecting the best model, comparing the proposed distribution with known distributions. A discrete analog of the HTLFR distribution is proposed.