On Quantile‐based Asymmetric Family of Distributions: Properties and Inference. (10th May 2019)

• Record Type: Journal Article
• Authors: Gijbels, Irène; Karim, Rezaul; Verhasselt, Anneleen
• Is Part Of: International statistical review. Volume 87:Number 3(2019)
• Page Start: 471
• Page End: 504
• Publication Date: 2019-05-10
• Subjects: Asymmetric density -- asymptotics -- location parameter -- maximum likelihood estimation -- method‐of‐moments -- quantiles; Statistics -- Periodicals; Statistics -- Bibliography -- Periodicals; Statistics -- Bibliography; Statistics -- Periodicals; Statistique; Statistique -- Périodiques; Statistique -- Bibliographie -- Périodiques; Statistique -- Étude et enseignement -- Périodiques; Statistique -- Étude et enseignement -- Bibliographie -- Périodiques; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519.2
• DOI: 10.1111/insr.12324
• Languages: English
• ISSNs: 0306-7734

Abstract

Summary: In this paper, we provide a detailed study of a general family of asymmetric densities. In the general framework, we establish expressions for important characteristics of the distributions and discuss estimation of the parameters via method‐of‐moments as well as maximum likelihood estimation. Asymptotic normality results for the estimators are provided. The results under the general framework are then applied to some specific examples of asymmetric densities. The use of the asymmetric densities is illustrated in a real‐data analysis.