Abstract
In this article, we introduce a new family of symmetric-asymmetric distributions based on skew distributions and on the family of order statistics with proportional hazards. This new family of distributions is able to fit both unimodal and bimodal asymmetric data. Furthermore, it contains, as special cases, the symmetric distribution and the “skew-symmetric” family, and therefore the skew-normal distribution. Another interesting feature of the family is that the parameter controlling the distributional shape in bimodal cases takes values in the interval (0, 1); this is an advantage for computing maximum likelihood estimates of model parameters, which is performed by numerical methods. The practical utility of the proposed distribution is illustrated in two real data applications.
Highlights
A seminal paper by [1] revealed the main properties of the “skew-normal” distribution whose probability density function is given by Academic Editors: Albert Shiryaev φSN (z; λ) = 2φ(z)Φ(λz), and Lev KlebanovReceived: 17 October 2021Accepted: 14 January 2022Published: 26 January 2022Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.z ∈ R, where Φ and φ denote the cumulative and density functions of the standard normal distribution, respectively
The study of asymmetric models based on order statistics goes back to [10], who introduced a model called the “Lehmann alternative”, which originated from the distribution of the maximum in the sample
We study the maximum likelihood (ML) estimators and the observed and expected information matrices for the parameters of the SPN model
Summary
Z ∈ R, where Φ and φ denote the cumulative and density functions of the standard normal distribution, respectively. Λ is a parameter that controls the asymmetry of the random variable Z. An important lemma demonstrated by [1] represents a fundamental result in the development of asymmetric and symmetric models for both unimodal and bimodal cases. Let f 0 be a pdf symmetrical around zero and a distribution function G such that G 0 exists and is a symmetric (around zero) density function; .
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call