Estimation of the Parameters of Wakeby Distribution by a Numerical Least Squares Method and Applying it to the Annual Peak Flows of Turkish Rivers

In this study, a numerical least squares (NLS) method for estimating the parameters of five-parameter Wakeby distribution was introduced. To asses the right tail estimate performances of the method, Monte Carlo simulated data and annual peak flows of 50 stations on Turkish rivers were used. Its results were compared to those by L-moments (LM) and curve fitting method of MATLAB. The biases from the LM for non-exceedence probability (F) of 0.999 mostly were less than those by the NLS. However, the values of relative root mean square error (rrmse) statistics from the NLS were better than those by the LM. In addition, the statistic of average deviation from the observed annual peak flows showed that NLS method exhibited mostly better results than those by LM for right tail predictions. Lastly, except the convergence problem of MATLAB, while both of the NLS and MATLAB produced the same determination coefficient (r <Superscript>2</Superscript>) for the majority of data set, the NLS produced lower rrmse values than MATLAB. Copyright Springer Science+Business Media B.V. 2011