A New Family of Archimedean Copulas: The Half-Logistic Family of Copulas

Abstract

In this research, we introduce a truncation of the half-logistic distribution function as a multiplicative Archimedean generator. The corresponding Archimedean copula is obtained, namely the half-logistic family. The dependency structure of this copula is distinct from other well-known ones. Kendall’s tau correlation coefficient is obtained in exact form and found to cover the entire positive dependence range (i.e., [0, 1]). We have proven that this copula is positively ordered and has no tail dependencies. The density of this copula is shown to be totally positive of order two. An extension of this copula is also introduced by adding a second parameter. This extension allows for a negative correlation and connects the famous Frank copula to the half-logistic copula. Two datasets were used to compare the half-logistic copula with some other known copula models.

Keywords

• copula
• Archimedean generator
• Archimedean copula
• cumulative distribution function
• half-logistic copula