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Estimating Cumulative Distribution Functions with Maximum Likelihood to Sample Data Sets of a Sea Floater Model
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 Title & Authors
Estimating Cumulative Distribution Functions with Maximum Likelihood to Sample Data Sets of a Sea Floater Model
Yim, Jeong-Bin; Yang, Won-Jae;
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This paper describes evaluation procedures and experimental results for the estimation of Cumulative Distribution Functions (CDF) giving best-fit to the sample data in the Probability based risk Evaluation Techniques (PET) which is to assess the risks of a small-sized sea floater. The CDF in the PET is to provide the reference values of risk acceptance criteria which are to evaluate the risk level of the floater and, it can be estimated from sample data sets of motion response functions such as Roll, Pitch and Heave in the floater model. Using Maximum Likelihood Estimates and with the eight kinds of regulated distribution functions, the evaluation tests for the CDF having maximum likelihood to the sample data are carried out in this work. Throughout goodness-of-fit tests to the distribution functions, it is shown that the Beta distribution is best-fit to the Roll and Pitch sample data with smallest averaged probability errors of 0.024 and 0.022, respectively and, Gamma distribution is best-fit to the Heave sample data with smallest of 0.027. The proposed method in this paper can be expected to adopt in various application areas estimating best-fit distributions to the sample data.
sea floater;risk evaluation;risk acceptance criteria;cumulative distribution function;maximum likelihood estimates;
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