The Lomax‐Claim Model: Bivariate Extension and Applications to Financial Data

Abstract

The uses of statistical distributions for modeling real phenomena of nature have received considerable attention in the literature. The recent studies have pointed out the potential of statistical distributions in modeling data in applied sciences, particularly in financial sciences. Among them, the two-parameter Lomax distribution is one of the prominent models that can be used quite effectively for modeling data in management sciences, banking, finance, and actuarial sciences, among others. In the present article, we introduce a new three-parameter extension of the Lomax distribution via using a class of claim distributions. The new model may be called the Lomax-Claim distribution. The parameters of the Lomax-Claim model are estimated using the maximum likelihood estimation method. The behaviors of the maximum likelihood estimators are examined by conducting a brief Monte Carlo study. The potentiality and applicability of the Lomax claim model are illustrated by analyzing a dataset taken from financial sciences representing the vehicle insurance loss data. For this dataset, the proposed model is compared with the Lomax, power Lomax, transmuted Lomax, and exponentiated Lomax distributions. To show the best fit of the competing distributions, we consider certain analytical tools such as the Anderson–Darling test statistic, Cramer–Von Mises test statistic, and Kolmogorov–Smirnov test statistic. Based on these analytical measures, we observed that the new model outperforms the competitive models. Furthermore, a bivariate extension of the proposed model called the Farlie–Gumble–Morgenstern bivariate Lomax-Claim distribution is also introduced, and different shapes for the density function are plotted. An application of the bivariate model to GDP and export of goods and services is provided.

Bivariate power Lomax distribution with medical applications

“…Our main statistical objective was to analyse a genuine dataset that is important in various domains using a fitting approach model. In this regard, we contrasted the suggested BFGMPLx distribution's fit with the BFGMWE and BFGMWITL mentioned by El-Sherpieny et al [24] and Bivariate FGM Lomax-Claim (BFGMLC) distribution which was mentioned by Zhao et al [40].…”

Investigating the Relationship between Processor and Memory Reliability in Data Science: A Bivariate Model Approach

“…Table 2 discusses different measures of goodness-of-fit, including AIC, CAIC, the BIC, and (HQIC), as well as the MLE estimator for the marginal parameters with SE. The comparison was performed for three models: BMExE, Bivariate Lomax-Claim (BLC), which was introduced by [41], bivariate Fréchet (BF) by [6], and bivariate Lomax (BL) by [42].…”

Bivariate Exponentiated Lomax Distribution Based on Marshall-olkin Method With a Real-life Application

“…Several studies have discussed bivariate distributions based on copulas. These include the works of Elgohari and Yousof [38], Hamed et al [39], Aboraya et al [40], El-Sherpieny et al [41], El-Sherpieny et al [42], El-Sherpieny et al [43], Almetwally et al [44], El-Sherpieny et al [45], Muhammed et al [46], Abulebda et al [47], Hassan et al [48], Zhao et al [49], and Qura et al [50].…”