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1	Comparison of Prediction Intervals for the Gumbel Distribution Fang, Lin 06 1900 (has links) <p> The problem of obtaining a prediction interval at specified confidence level to contain k future observations from the Gumbel distribution, based on an observed sample from the same distribution, is considered. An existing method due to Hahn, which is originally valid for the normal, is adapted to the Gumbel case. Motivated by the equivalence between Hahn's prediction intervals and Bayesian predictive intervals for the normal, we develop Bayesian predictive intervals for the Gumbel in the case where the scale parameter b is both known and unknown. Furthermore, we perform comparison of Hahn's and Bayesian intervals. We find that the Bayesian is better in the b known case, while Hahn and Bayes perform about the same in the other case when b is unknown. We then consider the maximum of the Hahn's and Bayesian predicted lower limits which is shown to be a better predictor when b is unknown. All the discussions are based on Monte Carlo simulations. In the end, the results are applied to Ontario Power Generation data on feeder thicknesses.</p> / Thesis / Master of Science (MSc)
2	Statistical Inference Chou, Pei-Hsin 26 June 2008 (has links) In this paper, we will investigate the important properties of three major parts of statistical inference: point estimation, interval estimation and hypothesis testing. For point estimation, we consider the two methods of finding estimators: moment estimators and maximum likelihood estimators, and three methods of evaluating estimators: mean squared error, best unbiased estimators and sufficiency and unbiasedness. For interval estimation, we consider the the general confidence interval, confidence interval in one sample, confidence interval in two samples, sample sizes and finite population correction factors. In hypothesis testing, we consider the theory of testing of hypotheses, testing in one sample, testing in two samples, and the three methods of finding tests: uniformly most powerful test, likelihood ratio test and goodness of fit test. Many examples are used to illustrate their applications. finite population correction factor statistical hypothesis type I error composite hypothesis power Central limit theorem Basu theorem critical value goodness of fit test likelihood ratio test Lehmann-Scheffe theorem complete statistic ancillary statistic P-value type II error Rao-Blackwell theorem simple hypothesis one-sided test two-sided test significance level sufficient statistic alternative hypothesis testing hypothesis null hypothesis rejection region confidence interval confidence level minimum variance unbiased estimator interval estimation uniformly most powerful test Cramer-Rao inequality likelihood function mean square error moment estimator error of estimation point estimation maximum likelihood estimator bias consistent estimator minimal sufficient statistic factorization theorem unbiased estimator statistic most powerful test test statistics Neyman-Pearson lemma decision rule

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Comparison of Prediction Intervals for the Gumbel Distribution

Statistical Inference