Asymptotic variance of flood quantile in log Pearson Type III distribution with historical information

Abstract Maximum likelihood and censored sample theory are applied for flood frequency analysis purposes to the log Pearson Type III (LP3) distribution. The logarithmic likelihood functions are developed and solved in terms of fully specified floods, historical information, and parameters to be estimated. The asymptotic standard error of estimate of the T -year flood is obtained using the general equation for the variance of estimate of a function. The variances and covariances of the parameters are obtained through inversion of Fisher's information matrix. Monte Carlo studies to verify the accuracy of the derived asymptotic expression for the standard errors of the 10, 50, 100, and 500 year floods, indicate that these are accurate for both Type I and Type II censored samples, while the bias is less than 2.5%. Subsequently, the Type II censored data were subjected to a random, multiplicative error. Results indicate that historical information contributes greatly to the accuracy of estimation of the quantiles even when the error of its measurement becomes excessive.