CONFIDENCE INTERVALS FOR THE SCALE PARAMETER OF A TWO-PARAMETER WEIBULL DISTRIBUTION: ONE SAMPLE PROBLEM

Abstract: The problem of interval estimating for the scale parameter θ in a two parameter Weibull distribution is addressed. The pivotal quantities whose percentiles can be used to construct confidence limits for the scale parameter θ are derived. Therefore in this paper, an exact, asymptotic and approximate (1−α)100% confidence intervals for the scale parameter θ of the two parameter Weibull distribution for the case of the one sample problem are derived. The three confidence intervals are simple and easy to compute. A Monte Carlo simulation study is performed to compare the efficiencies of the three confidence interval methods in terms of two criteria, coverage probabilities and average widths. The simulation results showed that the proposed confidence intervals perform well in terms of coverage probability and average width. Additionally, when the three methods are compared, it is found that the performance of the method depends on the value of the shape parameter β, scale parameters θ and sample size n used. The three methods are illustrated using a real-life data set which also supported the findings of the simulation study to some extent.