# Bayesian inference for multiple linear regression model under extended skew normal errors

A. A. Alhamedi, Kamarulzaman Ibrahim, M. T. Alodat, Nurulkamal Masseran

Research output: Contribution to journalArticle

### Abstract

In this paper, we conduct a study on the Bayesian inference for the multiple linear regression model when errors are assumed to follow the independent extended skew normal distribution. In the Bayesian inference, a hierarchal representation of the prior parameters is adopted in order to take advantage of the flexibility in the Bayesian methods. Then, we derive the posterior and full conditional posterior distribution. Furthermore, we conduct a simulation study to compare the parameter estimates found under the assumption that errors follow the extended skew normal distribution with their counterparts when the errors follow the multivariate normal distribution. Finally, we apply our findings to Australian Athletes data.

Original language English 171-187 17 Far East Journal of Mathematical Sciences 101 1 https://doi.org/10.17654/MS101010171 Published - 1 Jan 2017

### Fingerprint

Skew-normal Distribution
Multiple Linear Regression
Bayesian inference
Linear Regression Model
Skew
Model Error
Multivariate Normal Distribution
Bayesian Methods
Conditional Distribution
Posterior distribution
Flexibility
Simulation Study
Estimate

### Keywords

• Extended skew normal distribution
• Posterior distribution
• Simulation

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

In: Far East Journal of Mathematical Sciences, Vol. 101, No. 1, 01.01.2017, p. 171-187.

Research output: Contribution to journalArticle

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