A new Log-Lévy distribution with exponent parameter: Theory, properties, and utilization in the fields of accounting and radiation industries

Establishing the proper distributional assumptions of the data sets is necessary for parametric statistical conclusions and data set modelling. Therefore, the unpredictability and intricate patterns present in radiation data, especially lifetime data, are frequently difficult for classical probability models to reflect. The modelling of environmental pollutants in environmental science, the modelling of post-operative patient survival durations in medical science, and the modelling of software failure rates in computer science are just a few of the fields of study where statistical distributions are valuable. However, there are different levels of skewness and kurtosis in the data generation process. Additionally, non-monotonic failure rates, including bathtub, unimodal, or modified unimodal failure rates, could be present in the data. Therefore, using the current classical distributions to model the data does not yield an acceptable parametric fit and is frequently an estimate rather than a reality. The Log-Lévy distribution is presented as a solution to these constraints. More versatility is provided by this new model, which may depict a range of data features, including symmetric and skewed distributions, as well as various hazard rate patterns, including decreasing, increasing, and upside-down bathtub trends. Because of these characteristics, the Log-Lévy model can be used for statistical analysis in engineering and biological applications. The Log-Lévy distribution's moments, moment-generating function, entropy measures, quantile function, and order statistics are among the important characteristics that are derived in this study. The Log-Lévy model continuously obtains the lowest values for AIC, BIC, HQIC, and CAIC for some data sets, demonstrating its ideal trade-off between model complexity and goodness of fit. Further supporting the Log-Lévy model's resilience in capturing underlying data distributions is the fact that its Log-likelihood values are higher than those of the comparable model.