TESTS FOR MONOTONE FAILURE RATE BASED ON NORMALIZED SPACINGS
Abstract
Let X sub (1) < ... < X sub (n) be the order statistics of a random sample from a population with density f and distribution function F such that F(0) = 0. Let q(t) = f(t)/(1 - F(t)) be the failure rate of F. In testing H sub o: q(t) = lambda vs. H sub l: q(t) vertical arrow, Proschan and Pyke (Vth Berk. Symp.) considered certain statistics based on R sub l, ..., R sub n, the ranks of the normalized sample spacings D sub i = (n - i + l) (X sub (i) - X sub (i-l)), 1 = or < i = or < n, X sub (o) = 0. They show that these statistics are asymptotically normal for fixed F and compute the efficacy of one of these statistics for selected distributions. This report shows that asymptotic normality holds also for sequences of alternatives approaching H sub o as n approaches infinity and conclude that the above efficacies yield Pitman efficiencies.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1967
- Accession Number
- AD0661828
Entities
People
- Kjell A. Doksum
- Peter J. Bickel
Organizations
- University of California, Berkeley