Bimodal normal distribution: extensions and applications

Abstract

In this paper, a new family of continuous random variables with non-necessarily symmetric densities is introduced. Its density function can incorporate unimodality and bimodality features. Special attention is paid to the normal distribution which is included as a particular case. Its density function is given in closed-form which allows to easily compute probabilities, moments and other related measures such as skewness and kurtosis coefficients. Also, a stochastic representation of the family that enables us to generate random variates of this model is also presented. This new family of distributions is applied to explain the incidence of Hodgkin's disease by age. Other applications include the implications of bimodality in geoscience. Finally, the multivariate counterpart of this distribution is briefly discussed.