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On Quantile‐based Asymmetric Family of Distributions: Properties and Inference
Author(s) -
Gijbels Irène,
Karim Rezaul,
Verhasselt Anneleen
Publication year - 2019
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12324
Subject(s) - estimator , quantile , inference , normality , mathematics , maximum likelihood , asymptotic distribution , econometrics , estimation , quasi maximum likelihood , statistical physics , statistics , mathematical optimization , computer science , expectation–maximization algorithm , economics , artificial intelligence , physics , management
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.