A versatile bivariate distribution on a bounded domain: Another look at the product moment correlation

Samuel Kotz, J. Renévan Dorp
2002 Journal of Applied Statistics  
The Fairlie-Gumbel-Morgenstern (FGM) family has been investigated in detail for various continuous marginals such as Cauchy, normal, exponential, gamma, Weibull, lognormal and others. It has been a popular model for the bivariate distribution with mild dependence. However, bivariate FGM's with continuous marginals on a bounded support discussed in the literature are only those with uniform or power marginals. In this note we study the bivariate FGM family with marginals given by the recently
more » ... posed two-sided power (TSP) distribution. Since this family of bounded continuous distributions is very flexible, the properties of the FGM family with TSP marginals could serve a reliable indication of the structure of the FGM distribution with arbitrary marginals defined on a compact set. A remarkable stability of the correlation between the marginals has been observed.
doi:10.1080/0266476022000011247 fatcat:bk57uf6acrhmfgogy3gymon2dq