Idempotent copulas, m-dependence and Markov chains
Document Type
Lecture
Publication Date
10-3-2024
Abstract
New copula families are constructed following the ideas of Longla (2023). Subclasses of idempotent copulas with square integrable densities are derived. It is shown that these copulas generate exchangeable Markov chains that behave like independent and identically distributed random variables conditionally on the initiial variable. We prove that the extracted copula family is the only set of symmetric idempotent copulas with square integrable densities. We extend these copula families to asymmetric copulas with square integrable densities with special dependence properties. One of our extensions includes the Farlie-Gumbel-Morgenstern copula family (FGM). Mixing properties of Markov chains generated by these copulas follow from Longla (2022c) and Longla (2015). The Spearman’s correlation coefficient ρ is provided for each of these copula families. Some graphs are provided to illustrate the properties of the copula densities.
Relational Format
presentation
Recommended Citation
Longla, Martial, "Idempotent copulas, m-dependence and Markov chains" (2024). Probability & Statistics Seminar. 2.
https://egrove.olemiss.edu/math_statistics/2