The slashed Lomax distribution: new properties and Mellin-type statistical measures for inference

Several continuous distributions have been proposed recently to provide more flexibility in modeling lifetime data. Among these, the Slashed class of models, particularly the Slashed Lomax ( $\mathrm{SL}$ ) distribution, has gained special attention. This asymmetric model has positive support and it is notable for its stochastic representation and ability to fit heavy-tailed datasets. Despite the increasing number of new continuous models catering to specific samples, there have been few statistical tools introduced to evaluate their goodness-of-fits. To address this deficit, we employ the methodology outlined in J.M. Nicolas [Introduction aux statistiques de deuxième espèce: Applications des logs-moments et des logs-cumulants à l'analyse des lois d'images radar, TS, Trait. Signal 19 (2002), pp. 139-167] derived from the Mellin Transform (MT) to provide new goodness-of-fit measures for the $\mathrm{SL}$ distribution. These measures consider both qualitative and quantitative aspects. We derive the MT for the $\mathrm{SL}$ distribution, calculate the log-cumulants, and construct the log-cumulant diagram. Further, we introduce a test statistic using a combination of Hotelling's $T^2$ statistic and the multivariate Delta method to test hypotheses about the log-cumulants. We apply the new methodology to two real databases in the context of survival analysis to show its effectiveness in evaluating the fit criteria. We conduct bootstrap experiments to assess the power of the proposed test and to evaluate the performance of the estimators. The results revealed that the adjustment tools performed well and that the log-cumulant method proved to be an effective estimation criterion.