A Characterization of Exponential Distributions Through Conditional Independence
研究了在特定事件条件下，随机变量差值与后续变量的独立性等价于指数分布，为指数分布提供了新的刻画。
SUMMARY Let Y 1, Y 2, . . ., Yn be mutually independent non-negative random variables having an absolutely continuous distribution function Fi(y) over its support [0, ∞) and the corresponding density function f i(y) > 0 for y > 0. Let A denote the event that Yi – Y i+1 > 0 for all i = 1, 2, . . ., n – 1. Then we show that, conditional on the event A, Yi – Y i+1 and Y i+1 are independent for all i = 1, 2,. . ., k if and only if Yi (i = 1, 2, . . ., k) are exponentially distributed random variables, where 1 ≤ k ≤ n – 1. We note that the k exponential distributions can have different scale parameters.