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Interval Estimation in a Two Parameter Weibull Distribution Based on Type-2 Censored Data
Department of Mathematics, Egerton University, Egerton, Kenya
Department of Mathematics, Egerton University, Egerton, Kenya
Department of Mathematics, Egerton University, Egerton, Kenya
Department of Mathematics, Egerton University, Egerton, Kenya
- 1 Department of Mathematics, Egerton University, Egerton, Kenya
- 2 Department of Mathematics, Egerton University, Egerton, Kenya
- 3 Department of Mathematics, Egerton University, Egerton, Kenya
- 4 Department of Mathematics, Egerton University, Egerton, Kenya
Open Journal of Statistics·Volume 10 (2020)·Pages 1039–1056·Published 1 December 2020·DOI10.4236/ojs.2020.106059
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Abstract
In this paper, we consider the construction of the approximate profile- likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.
KeywordsTwo-Parameter Weibull DistributionInterval EstimationRelative Likelihood FunctionMaximum Relative Likelihood FunctionProfile-Likelihood IntervalCoverage Probability
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