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Comparison of Prediction Intervals for the Gumbel Distribution

<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)

Identiferoai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/21328
Date06 1900
CreatorsFang, Lin
ContributorsHoppe, Fred M., Statistics
Source SetsMcMaster University
Languageen_US
Detected LanguageEnglish
TypeThesis

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