Fitting Minima of Flows Via Maximum Likelihood

Abstract

A statistical method for deriving frequency distribution functions of minima of streamflows is presented. An innovative feature of the proposed methodology is that it does not require the specification of a parent distribution for streamflows, i.e., it is distribution free. The only assumption necessary is that the realizations of streamflows be independent, identically distributed random variables. The validity of this assumption is established with a nonparametric test. The main use of the methodology developed herein is in estimating small quantiles of the flow distribution for water supply planning and low‐flow investigations. An example is included to illustrate the applicability of the approach, using a record of annual flows.