On concomitants of order statistics arising from the extended Farlie–Gumbel–Morgenstern bivariate logistic distribution and its application in estimation

Philip, Anne; Thomas, P. Yageen

doi:10.1016/j.stamet.2015.02.002

Cited by 8 publications

(2 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this subsection, we use the economics data to illustrate the proposed model. We prove that the fit power of the FGMBL-Claim model is better than the 10 Complexity Farlie-Gumbel-Morgenstern bivariate Lomax (FGMBL) distribution [23]. e word "Better" is used in the sense that the FGMBL-Claim distribution has the smallest values of the considered fitting measures; this needs to be clarified; the details are given below.…”

Section: Modeling Of the Economics Datamentioning

confidence: 94%

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

et al. 2021

View full text Add to dashboard Cite

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.

show abstract

Section: Modeling Of the Economics Datamentioning

confidence: 94%

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

et al. 2021

View full text Add to dashboard Cite

show abstract

“…In the same sequence of advancements to the theory of concomitant of order statistics, Thomas and Veena (2011) defined the application of concomitant of order statistics in characterizing a family of bivariate distributions. Chacko and Thomas (2011) and Philip and Thomas (2015) extended the application of concomitant of order statistics in the estimation of parameters of Morgenstern type bivariate exponential distribution and extended Farlie-Gumbel-Morgenstern bivariate logistic distribution, respectively. In this study, the properties of concomitant of r th order statistics, i.e.…”

Section: Introductionmentioning

confidence: 99%

Concomitant of Order Statistics from New Bivariate Gompertz Distribution

Kumar

Khan

Kumar

2020

J. Mod. Appl. Stat. Methods

View full text Add to dashboard Cite

For the new bivariate Gompertz distribution, the expression for probability density function (pdf) of rth order statistics and pdf of concomitant arising from rth order statistics are derived. The properties of concomitant arising from the corresponding order statistics are used to derive these results. The exact expression for moment generating function (mgf) of concomitant of order rth statistics is derived. Also, the mean of concomitant arising from rth order statistics is computed using the mgf of concomitant of rth order statistics, and the exact expression for joint density of concomitant of two non-adjacent order statistics are derived.

show abstract