Response to the Letter to the Editor on ‘On Quantile‐based Asymmetric Family of Distributions: Properties and Inference’

Irène Gijbels, Rezaul Karim and Anneleen Verhasselt

International Statistical Review, 2020, vol. 88, issue 3, 797-801

Abstract: Rubio (2020) points out an identification problem for the four‐parameter family of two‐piece asymmetric densities introduced by Nassiri & Loris (2013). This implies that statistical inference for that family is problematic. Establishing probabilistic properties for this four‐parameter family however still makes sense. For the three‐parameter family, there is no identification problem. The main contribution in Gijbels et al. (2019a) is to provide asymptotic results for maximum likelihood and method‐of‐moments estimators for all members of the three‐parameter quantile‐based asymmetric family of distributions.

Date: 2020
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