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.

中文翻译：

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Lomax-Claim模型：双变量扩展及其在财务数据中的应用

在文献中，使用统计分布来模拟自然的真实现象已受到相当多的关注。最近的研究指出了统计分布在应用科学，特别是金融科学中的建模数据中的潜力。其中，两参数Lomax分布是著名的模型之一，可以非常有效地用于管理科学，银行，金融和精算科学等领域的数据建模。在本文中，我们通过使用一类索赔分布介绍了Lomax分布的新三参数扩展。新模型可以称为Lomax-Claim分布。使用最大似然估计方法估计Lomax-Claim模型的参数。通过进行简短的蒙特卡洛研究来检验最大似然估计器的行为。Lomax索赔模型的潜力和适用性通过分析表示车辆保险损失数据的金融科学数据集来说明。对于此数据集，将建议的模型与Lomax，功率Lomax，trans变Lomax和指数Lomax分布进行比较。为了显示竞争分布的最佳拟合，我们考虑使用某些分析工具，例如安德森-达林（Anderson-Darling）检验统计量，克雷默-冯·米塞斯（Cramer-Von Mises）检验统计量和科尔莫哥罗夫-斯米尔诺夫检验量统计量。基于这些分析方法，我们观察到新模型优于竞争模型。此外，还介绍了所提出模型的称为Farlie-Gumble-Morgenstern双变量Lomax-Claim分布的双变量扩展，并绘制了密度函数的不同形状。提供了将双变量模型应用于GDP以及商品和服务出口的信息。