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Physical Sciences and Mathematics Commons™
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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Probability Of Discrete Failures, Weibull Distribution, Mary Jo Hansen
Probability Of Discrete Failures, Weibull Distribution, Mary Jo Hansen
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
The intent of this research and these is to describe the development of a series of charts and tables that provide the individual and cumulative probabilities of failure applying to the Weibull statistical distribution. The mathematical relationships are developed and the computer programs are described for deterministic and Monte Carlo models that compute and verify the results. Charts and tables reflecting the probabilities of failure for a selected set of parameters of the Weibull distribution functions are provided.
Computer Program Generation Of Extreme Value Distribution Data, Stephen (Wan-Tsing) Lei
Computer Program Generation Of Extreme Value Distribution Data, Stephen (Wan-Tsing) Lei
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
The application of the Monte Carlo method on the estimation in Gumbel extreme value distribution was studied. The Gumbel extreme value distribution is used to estimate the flood flow of specific return period for the design of flood mitigation project. This paper is a programming effort (1) to estimate the parameters of Gumbel distribution using the observed data and (2) to provide a random variate generating subroutine to generate random samples and order statistics of a Gumbel distribution random variable. The mean squared error is used to measure the accuracy of the estimation method. Finally, an example of the use …
Least Squares Estimation Of The Pareto Type I And Ii Distribution, Ching-Hua Chien
Least Squares Estimation Of The Pareto Type I And Ii Distribution, Ching-Hua Chien
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
The estimation of the Pareto distribution can be computationally expensive and the method is badly biased. In this work, an improved Least Squares derivation is used and the estimation will be less biased. Numerical examples and figures are provided so that one may observe the solution more clearly. Furthermore, by varying the different methods of estimation, a comparing of the estimators of the parameters is given. The improved Least Squares derivation is confidently employed for it is economic and efficient.
Extreme Value Distribution In Hydrology, Bill (Tzeng-Lwen) Chen
Extreme Value Distribution In Hydrology, Bill (Tzeng-Lwen) Chen
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
The problems encountered when empirical fit is used as the sole criterion for choosing a distribution to represent annual flood data are discussed. Some theoretical direction is needed for this choice. Extreme value theory is established as a viable tool for analyzing annual flood data. Extreme value distributions have been used in previous analyses of flood data. However, no systematic investigation of the theory has previously been applied. Properties of the extreme value distributions are examined. The most appropriate distribution for flood data has not previously been fit to such data. The fit of the chosen extreme value distribution compares …