On some properties of the bimodal normal distribution and its bivariate version

In this work, we derive some novel properties of the bimodal normal distribution. Some of its mathematical properties are examined. We provide a formal proof for the bimodality, present a stochastic representation, and assess identifiability. We also provide a closed formula for the moments of the bimodal normal distribution. We then discuss the max- imum likelihood estimates as well as the existence of these estimates, and also some asymptotic …