Interval Estimation for Weibull distribution based on a sample of size one

摘要

In this paper, we demonstrate the method of construction of 100(1 - δ)% confidence interval for parameter λ (scale parameter) of a Weibull distribution based on a sample of size one. We take a cue from this method to construct a similar 100(1 - δ)% confidence intervals for these parameters based on X_(1:n) = min{X_1,X_2,hell,X_n} where X_1,X_2,hell,X_n are n(≥ 2) independent random variables from a Weibull distribution having parameters λ β For β = 1, i.e. for exponential distribution, although the proposed confidence interval for the mean λ overlaps with the confidence interval based on chi-square distribution, the former one is significantly narrower than the latter one. For n ≥ 2 additional numerical results that compare proposed 100(1 - δ)% confidence intervals for λ with the ones that are given in Bain and Engelhardt (1991) are provided. It is interesting to note that the former ones turn out to be significantly narrower than the latter ones for samples of sizes 1 through 5 for δ = 0.02, 0.05 and 0.10.