Symmetric and Asymmetric Distributions Theoretical Developments and Applications

• Other Authors: Gómez Déniz, Emilio (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2020
• Subjects: Humanities; Social interaction; positive and negative skewness; ordering; fitting distributions; Epsilon-skew-Normal; Epsilon-skew-Cauchy; bivariate densities; generalized Cauchy distributions; asymmetric bimodal distribution; bimodal; maximum likelihood; slashed half-normal distribution; kurtosis; likelihood; EM algorithm; flexible skew-normal distribution; skew Birnbaum-Saunders distribution; bimodality; maximum likelihood estimation; Fisher information matrix; maximum likelihood estimates; type I and II censoring; skewness coefficient; Weibull censored data; truncation; half-normal distribution; probabilistic distribution class; normal distribution; identifiability; moments; power-normal distribution
• Online Access: DOAB: download the publication; DOAB: description of the publication

In recent years, the advances and abilities of computer software have substantially increased the number of scientific publications that seek to introduce new probabilistic modelling frameworks, including continuous and discrete approaches, and univariate and multivariate models. Many of these theoretical and applied statistical works are related to distributions that try to break the symmetry of the normal distribution and other similar symmetric models, mainly using Azzalini's scheme. This strategy uses a symmetric distribution as a baseline case, then an extra parameter is added to the parent model to control the skewness of the new family of probability distributions. The most widespread and popular model is the one based on the normal distribution that produces the skewed normal distribution. In this Special Issue on symmetric and asymmetric distributions, works related to this topic are presented, as well as theoretical and applied proposals that have connections with and implications for this topic. Immediate applications of this line of work include different scenarios such as economics, environmental sciences, biometrics, engineering, health, etc. This Special Issue comprises nine works that follow this methodology derived using a simple process while retaining the rigor that the subject deserves. Readers of this Issue will surely find future lines of work that will enable them to achieve fruitful research results.