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.
Highlights
Introduction e Lomax or ParetoII distribution was proposed by Lomax in the mid of the last century to model business failure data. is model has a wide range of applications in a variety of fields, in income and wealth inequality, size of cities, and financial and actuarial sciences
We introduce a new three-parameter extension of the Lomax distribution via using a class of claim distributions. e new model may be called the Lomax-Claim distribution. e parameters of the Lomax-Claim model are estimated using the maximum likelihood estimation method. e behaviors of the maximum likelihood estimators are examined by conducting a brief Monte Carlo study. e potentiality and applicability of the Lomax claim model are illustrated by analyzing a dataset taken from financial sciences representing the vehicle insurance loss data
In the context lifetime scenario, the Lomax distribution falls under the domain of decreasing failure rate distributions. is distribution has been proved as a significant alternative to the exponential, Weibull, and gamma distributions to model heavy-tailed data sets
Summary
We study a three-parameter L-Claim distribution and investigate the shapes of its pdf. e cdf and pdf of the L-Claim distribution can be obtained by substituting expressions (1) and (2) in (3) and (4), respectively. We study a three-parameter L-Claim distribution and investigate the shapes of its pdf. Due to the right-skewed and heavy-tailed behavior of the proposed model, it can be a good candidate model for modeling heavy-tailed data which are very important in financial and actuarial sciences. The two-parameter traditional Lomax distribution belongs to the class of decreasing failure rate distributions. From the plots provided, it is clear that the L-Claim distribution has unimodal and increasing failure rate functions. Besides the heavy-tailed behavior, this is another superiority of the proposed model over the Lomax distribution
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