标题： 圆上的卡迪oid分布的扩展 显示英文标题

标题： An Extension of the Cardioid Distributions on Circle

摘要： 一种新的圆上的分布族被引入，它是Cardioid分布的推广。 计算了均值、方差和特征函数等基本性质。 该分布要么是单峰的，要么是双峰的。 计算了众数。 描述了该分布的对称性。 证明了参数是规范的（即由分布唯一确定）。 我们还表明，这个新的族是傅里叶级数次数至多为2的分布的一个子集，并研究了这一性质的含义。 显示英文摘要

摘要： A new family of distributions on the circle is introduced which are a generalization of the Cardioid distributions. The elementary properties such as mean, variance and the characteristic function are computed. The distribution is either unimodal or bimodal. The modes are computed. The symmetry of the distribution is characterized. The parameters are shown to be canonic (i.e. uniquely determined by the distribution). We also show that this new family is a subset of distributions whose Fourier series has degree at most 2 and study the implications of this property.