ON A TEST FOR GENERALIZED UPPER TRUNCATED WEIBULL-DISTRIBUTIONS

Abstract

We study upper truncated Weibull random variables with density given by g-beta,delta,tau(t) = beta-delta-t-delta-1 exp(-beta-t-delta)(1 - exp(-beta-tau-delta))-1 for 0 less-than-or-equal-to t less-than-or-equal-to tau (tau is the truncation parameter), delta > 0 and beta is-an-element-of R. Denoting by beta triple-overdot, delta triple-overdot and tau triple-overdot the maximum likelihood estimators we show that sign(beta triple-overdot) = sign(1/2 - G(n)), where G(n) = (1/n)SIGMA-i =1n(T(i)/tau triple-overdot) delta triple-overdot. It is also shown that 4 square-root 3n(1/2 - G(n)(beta = 0)) converges to a normalized Guassian. This result is then used to provide a test for the hypothesis-beta = 0.