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.
翻译：在这项工作中,我们得出了双模式正常分布的一些新特性。 一些数学特性经过了检查。 我们为双模式提供了正式的证明, 并评估了可识别性。 然后我们讨论了最大可能性的估计数以及这些估计数的存在情况, 以及控制双模式的参数估计器的一些无症状性能。 生成了双轨版本的BN分布, 并分析了一些特性, 如共差和关联性。 我们研究了静态性、 惯性以及三角阵列中心定理。 最后, 进行了蒙特卡洛研究, 以评估最大可能性估计的性能 。
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