Fitting Procedures for the Log‐Boughton Distribution

The paper describes a procedure for direct, optimal fitting of the log‐Boughton frequency distribution to either complete sets or subsets of annual flood data. The analytical basis and derivation of the procedure are given. Annual floods from 65 yr of record on the $5\text{,}755‐{\mathrm{km}}^2$ Santa Cruz River at Tucson, Arizona, are used to show the fitting of the distribution to a complete data set, and annual floods from 24 yr of record on the $149‐{\mathrm{km}}^2$ Walnut Gulch watershed, in southeastern Arizona, are used to show the fitting of the distribution to a subset of data. Substantial differences between the log‐Boughton and log‐Pearson type 3 distributions occur in fitting to the Walnut Gulch data, due mainly to the large negative skew coefficient $(-2.83)$ of this data set. The computer program which fits the log‐Boughton distribution plots the data points on a probability paper which is automatically scaled to linearize the fitted distribution.