Confidence Intervals for Design Events

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Abstract
Confidence intervals for normal, lognormal, and Pearson Type III quantiles based on asymptotic theory are shown to fail to contain the true 100‐year flood and other design events with the specified frequency (confidence level). Intervals which contain normal or lognormal quantiles with the desired confidence can be constructed using the noncentral t‐distribution. Tables are provided. An adjustment for the case when a variable has a Pearson Type III distribution with known skewness coefficient is suggested. Such intervals are shown to contain design events with nearly the desired level of confidence. Confidence intervals constructed using the U.S. Water Resources Council guidelines, Bulletins 17A and 17B, often did not achieve the desired confidence level.