Statistical properties of the Odd Lomax Burr Type X distribution with applications to failure rate and radiation data

Abstract

This article introduces the Odd Lomax Burr Type X (OLoBX) distribution, an extension of the four-parameter Burr Type X model. The Quantile function, moments, the function that generates the moments, Rényi entropy, and the ordered statistics are some of the new distribution's essential statistical aspects. For the purpose of estimating the parameters of the new distribution, the technique of maximum likelihood estimation is used. Monte Carlo simulation examines the estimators' performance and reveals that the maximum likelihood technique is effective in parameter estimation. The OLoBX distribution was used on the electrical relay failure time, fatigue fracture life, and radiation data sets to test its adaptability and flexibility, it outperformed its sub models and other popular distributions. The new distribution showed high flexibility in representing heavy-tailed and asymmetric data, outputforming well-known distributions such as TEEBX, BeBX, and WeBX. Monte Carlo simulations demonstrated that MLE estimation of OLoBX parameters is satable and accurate, especially at large sample size (n = 300), where the RMSE and Abias values decreased significantly. The OLoBX distribution outperformed competing distributions in terms of goodness-of-fit criteria, confirming its effectiveness in modeling real data.