A five-parameter distribution called the McDonald normal distribution is defined and studied. The new distribution contains, as special cases, several important distributions discussed in the literature, such as the normal, skew-normal, exponentiated normal, beta normal and Kumaraswamy normal distributions, among others. We obtain its ordinary moments, moment generating function and mean deviations. We also derive the ordinary moments of the order statistics. We use the method of maximum likelihood to fit the new distribution and illustrate its potentiality with three applications to real data.

翻译：定义和研究称为麦当劳正常分布的5个参数分布。新分布作为特殊情况,包含文献中讨论的几种重要分布,例如正常、扭曲正常、排出正常、贝塔正常和库马拉斯瓦米正常分布等。我们获得其普通时刻、瞬时生成功能和平均偏差。我们还得出命令统计的普通时刻。我们使用最可能的方法来适应新的分布,并用三个应用程序来说明其潜力与真实数据。