On a test for generalized upper truncated Weibull distributions

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- for 0[less-than-or-equals, slant]t[less-than-or-equals, slant][tau] ([tau] is the truncation parameter), [delta]>0 and [beta] [epsilon] . Denoting by , and the maximum likelihood estimators we show that sign()=sign(-Gn), where Gn=(1/n)[Sigma]ni=1(Ti/). It i Gaussian. This result is then used to provide a test for the hypothesis [beta] = 0.