Efficient Estimation of the PDF and the CDF of the Weibull Extension Model |
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| Authors: | S F Bagheri S Nadarajah E Deiri |
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| Institution: | 1. Department of Mathematics, College of Basic Science, Yadegar-e-lmam Khomeini (RAH) Branch, Islamic Azad University, Tehran, Iran;2. School of Mathematics, University of Manchester, United Kingdom;3. Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran |
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| Abstract: | The Weibull extension model is a useful extension of the Weibull distribution, allowing for bathtub shaped hazard rates among other things. Here, we consider estimation of the PDF and the CDF of the Weibull extension model. The following estimators are considered: uniformly minimum variance unbiased (UMVU) estimator, maximum likelihood (ML) estimator, percentile (PC) estimator, least squares (LS) estimator, and weighted least squares (WLS) estimator. Analytical expressions are derived for the bias and the mean squared error. Simulation studies and real data applications show that the ML estimator performs better than others. |
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| Keywords: | Least squares estimator Maximum likelihood estimator Model selection criteria Percentile estimator Uniform minimum variance unbiased estimator Weibull extension model Weighted least squares estimator |
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