Testing whether a survival distribution is new better than used of an unknown specified age

Abstract

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 ) when the point to is unknown but can be estimated from the data is proposed when t 0 = μ, the mean of F , and also when t 0 = ξ p , the p th percentile of F . It is shown that, while the known tests for known t 0 (Hollander, Park & Proschan, 1986; Ebrahmi & Habibullah, 1990) continue to hold when t 0 = μ and is estimated by X ¯ ⁠ , a simpler and distributionfree test is possible when t 0 = ξ p and is estimated by X ([n,p]) . The performance of this test is presented.