One of the structural properties of distributions is their unimodality, which can be seen in the form of a function, such as skewness, kurtosis, and symmetry. When comparing two completely different distributions, a statistician will have a very difficult task, but if both distributions are of the same type, for example, both are unimodal, it is enough to compare the modes, dispersions, and skewnesses to compare them. Therefore, the concept of unimodality and its generalization, a-unimodality of distributions, and their specification in comparing two distributions are of great importance. Throughout this article, we will examine the concept of unimodality and its generalization, i.e. a-unimodality, for continuous and discrete random variables, and then we will examine the concept of uniformity and a-uniformity of distributions, which are another property of distributions. Also, in the end, we will present the application of discrete a-unimodal distributions in finding the upper bound of the variance.