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• W799601903 abstract "This thesis presents simple efficient algorithms to estimate distribution parameters and to construct prediction intervals for location–scale families. Specifically, we study two scenarios: one is a frequentist method for a general location–scale family and then extend to a 3–parameter distribution, another is a Bayesian method for the Gumbel distribution. At the end of the thesis, a generalized bootstrap resampling scheme is proposed to construct prediction intervals for data with an unknown distribution. Our estimator construction begins with the equivariance principle, and then makes use of unbiasedness principle. These two estimates have closed form and are functions of the sample mean, sample standard deviation, sample size, as well as the mean and variance of a corresponding standard distribution. Next, we extend the previous result to estimate a 3-parameter distribution which we call a mixed method. A central idea of the mixed method is to estimate the location and scale parameters as functions of the shape parameter. The sample mean is a popular estimator for the population mean. The mean squared error (MSE) of the sample mean is often large, however, when the sample size is small or the scale parameter is greater than the location parameter. To reduce the MSE of our location estimator, we introduce an adaptive estimator. We will illustrate this by the example of the power Gumbel distribution. The frequentist approach is often criticized as failing to take into account the uncertainty of an unknown parameter, whereas a Bayesian approach incorporates such uncertainty. The present Bayesian analysis for the Gumbel data is achieved numerically as it is hard to obtain an explicit form. We tackle the problem by providing an approximation to the exponential sum of Gumbel random variables." @default.
• W799601903 created "2016-06-24" @default.
• W799601903 creator A5081333381 @default.
• W799601903 date "2014-01-01" @default.
• W799601903 modified "2023-09-27" @default.
• W799601903 title "Parameter Estimation and Prediction Interval Construction for Location-Scale Models with Nuclear Applications" @default.
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• W799601903 hasPublicationYear "2014" @default.
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