平衡分布与寿命分布类

Equilibrium distribution and the class of life distribution

平衡分布给出了L分布类一个新的定义方式,并证明新定义与原定义等价.研究了平衡分布的一些性质,通过寿命的平衡分布与指数分布在Laplace变换下的比较,得到一种判定L(L)类寿命分布的方法.进一步用平衡变量Xe的期望与寿命X的期望作比较提出一种新的寿命分布类———E类,研究了E类与其他寿命分布类之间的蕴含关系,证明了E类是比L类更大的一个分布类.最后讨论了E类在卷积下的封闭性质.

A new definition of L class is given by the equilibrium distribution and proved to be equivalent to the old one. Some properties of equilibrium distribution is analyzed and a method for judging L() class distribution is provided through the comparison of equilibrium distribution and exponential distribution under Laplace transform. Further more, we present a new class of life distribution — E class which bases on the comparison of the expectation of X and X_e. The relationship between E class and other class is discussed and we prove that the E class is larger than L class. At last, the closure property of L class under convolution is proved.