On the joint distribution of placement statistics under progressive censoring and applications to precedence test

• Published in: Journal of statistical planning and inference Vol. 138; no. 5; pp. 1314 - 1324
• Main Authors: Balakrishnan, N., Tripathi, Ram C., Kannan, Nandini
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.05.2008; New York,NY Elsevier Science; Amsterdam
• Subjects: Distribution theory; Exact sciences and technology; General topics; Mathematics; Nonparametric inference; Nonparametric tests of homogeneity; Placements; Precedence and exceedance statistics; Probability and statistics; Probability theory and stochastic processes; Progressive Type-II censoring; Sciences and techniques of general use; Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications); Statistics; Wilcoxon rank-sum test; Nonparametric tests of homogeneity; Placements; Wilcoxon rank-sum test; Progressive Type-II censoring; Precedence and exceedance statistics; Statistical distribution; Sample size; L statistics; Censored sample; Significance level; Equality test; Industry; F distribution; Hypothesis test; Engineering; Statistical test; Survival function; Distribution function; Approximation theory; Sample survey; Exact distribution; Censored data; Test statistic; Statistical decision; Life test; Joint distribution; Survival; Statistical method; Survival analysis; Lifetime; Sampling theory; Reliability
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2007.06.018

In reliability and survival analysis, comparison of two or more populations is an important problem. For example, while comparing a treatment group with a control group, one may be interested in determining whether the observations in the treatment group have a longer lifetime than those from the control group, that is, whether the treatment is effective or not. In such a study, it would be extremely valuable to make a decision based on early failures. In this paper, we consider independent progressively Type-II censored random samples from two populations with cumulative distribution function's (cdf) F ( · ) and G ( · ) respectively, and discuss a precedence test for testing the equality of the two distributions based on placements. For this purpose, we derive the joint distribution of the first l placement statistics from the progressively censored sample from F ( · ) . We then derive the exact null distribution of the precedence test statistic which is simply the sum of the placements. We provide the rejection regions for fixed levels of significance and various sample sizes and different progressive censoring schemes.