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Numerical Investigations on Plotting Formulas and Confidence Intervals of Return Values in Extreme statistics

Publication year Port and Airport Research Institute Report 027-01-02 1988.03
Author(s) Yoshimi GODA
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Executive Summary

Numerical experiments by Monte Carlo simulations are carried out to give answers to the problems of plotting-position formulas, confidence intervals of parameter estimates, uncertainty of return values due to sampling variability and not-knowing true distribution functions, and others. The FT-I type, the log-normal,and the Weibull (k=0.75, 1.0, 1.4, and 2.0) distributions are tested by drawing 10,000 samples with the size ranging from 10 to 100, for both uncensored and censored data (censoring rate 1/2 and 1/4).
 The Gringorten, the Blom, and the modified Petruaskas and Aagaard plotting-formulas are confirmed to be the best for the above distribution functions, respectively. The standard deviations of the estimated return values are synthesized into empirical formulas for the both cases where the true distribution function is known and unknown. The latter case yields a bias on the estimate of return values and empirical formulas are given for its correction.

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