CONFIDENCE INTERVALS FOR THE SCALE PARAMETER
OF A TWO-PARAMETER WEIBULL DISTRIBUTION: ONE SAMPLE PROBLEM
Moustafa O.A. Abu-Shawiesh, Juthaphorn Sinsomboonthong2,
Ahmad M.A. Adawi3, Mohammad H. Almomani4 1 Department of Mathematics, Faculty of Science
The Hashemite University, Al-Zarqa, 13115, JORDAN 2 Department of Statistics, Faculty of Science
Kasetsart University, Bangkok, 10900, THAILAND 3 Department of Mathematics, Faculty of Science
The Hashemite University, Al-Zarqa, 13115, JORDAN 4 Department of Mathematics, Faculty of Science
The Hashemite University, Al-Zarqa, 13115, JORDAN
The problem of interval estimating for the scale parameter in a two parameter Weibull distribution is addressed. The pivotal quantities whose percentiles can be used to construct confidence limits for the scale parameter are derived. Therefore in this paper, an exact, asymptotic and approximate
confidence intervals for the scale parameter 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 , scale parameters and sample size used. The three methods are illustrated using a real-life data set which also supported the findings of the simulation study to some extent.
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