Miscellanea. Testing whether a survival distribution is new better than used of an unknown specified age
本文提出一种检验生存分布是否在未知指定年龄上优于使用中新分布的方法，当指定年龄为均值或百分位数时，给出了相应的检验统计量，并证明当指定年龄为中位数时存在更简单的无分布检验。
A survival variable is a nonnegative random variable X with distribution function F and a survival function F = 1 - F. This variable is said to be new better than used of specified age t 0 if F(x + t 0 ) ≤ F(x)F(t 0 ) for all x ≥ 0 and a fixed t 0 . Testing H 0 : F(x + t 0 ) = F(x)F(t 0 ) for all x ≥ 0 against H 1 : F(x + t 0 ) ≤ F(x)F(t 0 ) for x ≥ 0 when the point t 0 is unknown but can be estimated from the data is proposed when t 0 = p, the mean of F, and also when t 0 = ζ p , the pth percentile of F. It is shown that, while the known tests for known t 0 (Hollander, Park & Proschan, 1986; Ebrahimi & Habibullah, 1990) continue to hold when t 0 = μ and is estimated by X, a simpler and distribution-free test is possible when t 0 = ζ p and is estimated by X ([np]) . The performance of this test is presented.