A Unified Approach for Construction of Probability Models for Bivariate Linear and Directional Data

Abstract

This article considers a unified approach based on the mixture method to construct linear bivariate models and those on the cylinder and torus involving the exponential and cardioid distributions with the truncated exponential distribution as the mixing distribution. Parameter estimation of the bivariate model on the torus is considered for the data set of phase angles of circadian-related genes in heart and liver tissues.

Keywords:

• Cardioid
• Exponential
• Truncated exponential
• Distribution on cylinder and torus
• Mixture models

Mathematics Subject Classification:

• 60E05
• 62H11
• 62H12