A Quantile-Based Asymmetric Family of Distributions: Inference

• Activity Number: 627 - Advances in Stochastics and Distribution Theory
• Type: Contributed
• Date/Time: Thursday, August 2, 2018 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Anneleen Verhasselt* and Karim Rezaul and Irene Gijbels
• Companies: Hasselt University and Hasselt University and KU Leuven and KU Leuven
• Keywords: asymmetric density; location parameter; quantiles; maximum likelihood estimation; method-of-moments

Abstract

We study a general family of asymmetric densities. Within this family, we derive the expressions for important characteristics of the distributions (such as quantile function, moments, skewness, kurtosis) and discuss the estimation of the parameters via method-of-moments as well as maximum likelihood estimation. We apply the results on some specific examples of asymmetric densities (asymmetric normal, students-t, Laplace, logistic). The use of the asymmetric densities is illustrated in a data analysis.