Baker- Lin-Huang type Bivariate distributions based on order statistics

TL;DR

This paper introduces a new class of bivariate distributions based on order statistics and copulas, achieving higher correlations than previous models, expanding the flexibility of dependence modeling.

Contribution

It constructs Baker-type bivariate distributions using arbitrary copulas, enabling higher correlations and broader dependence structures than existing models.

Findings

New class of distributions with high correlation

Use of arbitrary copulas enhances dependence modeling

Achieves correlations beyond previous Baker distributions

Abstract

Baker (2008) introduced a new class of bivariate distributions based on distributions of order statistics from two independent samples of size n. Lin-Huang (2010) discovered an important property of Baker's distribution and showed that the Pearson's correlation coefficient for this distribution converges to maximum attainable value, i.e. the correlation coefficient of the Frech\'et upper bound, as n increases to infinity. Bairamov and Bayramoglu (2011) investigated a new class of bivariate distributions constructed by using Baker's model and distributions of order statistics from dependent random variables, allowing high correlation than that of Baker's distribution. In this paper a new class of Baker's type bivariate distributions with high correlation are constructed on the base of distributions of order statistics by using an arbitrary continuous copula instead of the product copula. Keywords: Bivariate distribution function, FGM distributions, copula, positive quadrant dependent, negative quadrant dependent, order statistics, Pearson's correlation coefficient.