English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Skewed generalizations of the normal distribution have been a topic of greatinterest in the statistics community due to their diverse applications acrossseveral domains. One of the most popular skew normal distributions, due to itsintuitive appeal, is the Azzalini's skew normal distribution. However, due tothe nature of the distribution it suffers from serious inferential problems.Interestingly, the Bayesian approach has been shown to mitigate these issues.Recently, another skew normal distribution, the Geometric skew normaldistribution, which is structurally different from Azzalini's skew normaldistribution, has been proposed as an alternative for modelling skewed data.Despite the interest in skew normal distributions, a limited number of articlesdeal with comparing the performance of different skew distributions, especiallyin the Bayesian context. To address this gap, the article attempts to comparethese two skew normal distributions in the Bayesian paradigm for modelling datawith varied skewness. The posterior estimates of the parameters of thegeometric skew normal distribution are obtained using a hybrid Gibbs-Metropolisalgorithm and the posterior predictive fit to the data is also obtained.Similarly, for the Azzalini's skew normal distribution, the posteriorpredictive fit are derived using a Gibbs sampling algorithm. To compare theperformance, Kolmogorov-Smirnov distance between the posterior predictivedistribution and original data is utilised to measure the goodness of fit forboth the models. An assortment of real and simulated data sets, with a widerange of skewness, are analyzed using both the models and the advantages aswell as disadvantages of the two models are also discussed. Finally, a muchfaster Variational Bayes method for approximating the posterior distribution ofthe geometric skew normal model is proposed and its performance is discussed.

Comparison of Azzalini and Geometric Skew Normal Distributions Under Bayesian Paradigm