Some results on normalized total time on test and spacings

✍ Scribed by Nader Ebrahimi; Fabio Spizzichino

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 532 KB
• Volume: 36
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(97)00068-0

✦ Synopsis

Let Y~,Y2,...,Yn be non-negative random variables and let Yo)~< Y(2)~ "'" ~ Y(n) denote order statistics. In this manuscript, we study several properties of Di = (n-i + 1 )( Y~i) -Y(i-1) ), i = 1,2 .... , n, where Y(0) = 0. In particular we characterize the relevant case of lifetimes with Schur-constant density in terms of the joint density function of D1,... ,D,. We also analyze properties of Schur-concave (convex) densities and of the functions #(i) = E {Di} and h(i) = (1/i) ~=~ g(j).