Testing uniform stochastic ordering for survival functions

• Published in: Communications in statistics. Theory and methods Vol. 29; no. 7; pp. 1649 - 1661
• Main Authors: Singh, Harshinder, Singh, R.S., Qian, Shixian
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Marcel Dekker, Inc 01.01.2000; Taylor & Francis
• Subjects: Applications; Exact sciences and technology; Markov processes; Mathematics; Multivariate analysis; Nonparametric inference; Probability and statistics; Probability theory and stochastic processes; Reliability, life testing, quality control; Sciences and techniques of general use; Statistics; Kolmogorov Smirnov test; Gaussian distribution; Order statistic; Stochastic ordering; Multiple comparison; Stochastic process; Hypothesis test; Statistical test; Lifetime; Survival function; Limit distribution; Maximum likelihood; Reliability
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610920008832570

Let and be the survival functions of lifetimes of two units under study. F is said to be uniformly stochastically smaller than G, denoted by F < + G, if (x)/& (x) is a nondecreasing function, In this paper, we construct some tests for testing the null hypothesis H 0 :F=G against H a : F < + G and F ≠ G,where G is a known cdf, A test based on the estimator of Rojo and Samaniego ( 1993 ) turns out to be the Kolmogorov-Smirnov test D n + , indicating suitability of D n + , for testing H 0 against H a , Power comparisons of these tests and that of Kochar(i984) have been made for some specific H 0 and H a , The above testing procedures have been applied to a data set of observed lifetimes of Kevlar H epoxy pressure vessels.