  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 and assess identifiability. We then discuss the
maximum likelihood estimates as well as the existence of these estimates, and
also some asymptotic properties of the estimator of the parameter that controls
the bimodality. A bivariate version of the BN distribution is derived and some
characteristics such as covariance and correlation are analyzed. We study
stationarity and ergodicity and a triangular array central limit theorem.
Finally, a Monte Carlo study is carried out for evaluating the performance of
the maximum likelihood estimates.
