A Bimodal Extension of the Log-Normal Distribution on the Real Line with an Application to DNA Microarray Data

Abstract

A bimodal double log-normal distribution on the real line is proposed using the random sign mixture transform. Its associated statistical inferences are derived. Its parameters are estimated by the maximum likelihood method. The performance of the estimators and the corresponding confidence intervals is checked by simulation studies. Application of the proposed distribution to a real data set from a DNA microarray is presented.

Keywords

• bimodality
• log-normal distribution
• maximum likelihood estimation
• Monte Carlo simulations