# Bayesian modelling of skewness and kurtosis with two-piece scale and shape distributions

arXiv: https://arxiv.org/abs/1406.7674 · HTML: https://mlsanity.com/paper/1406.7674/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2014.

## Built on by (most cited first, 1 of 1)

- [A Monotone Single-Index Modal Regression Powered by Deep Neural Networks for Non-Gaussian Periodontal Data](https://mlsanity.com/paper/2505.02153/) (2025)

## Abstract (arXiv)

We formalise and generalise the definition of the family of univariate double two--piece distributions, obtained by using a density--based transformation of unimodal symmetric continuous distributions with a shape parameter. The resulting distributions contain five interpretable parameters that control the mode, as well as the scale and shape in each direction. Four-parameter subfamilies of this class of distributions that capture different types of asymmetry are discussed. We propose interpretable scale and location-invariant benchmark priors and derive conditions for the propriety of the corresponding posterior distribution. The prior structures used allow for meaningful comparisons through Bayes factors within flexible families of distributions. These distributions are applied to data from finance, internet traffic and medicine, comparing them with appropriate competitors.