Parameter Estimation for Some Probability Distributions Used in Hydrology

Abstract

Estimating the parameters of probability distributions generally involves solving a system of nonlinear equations or a nonlinear equation, being a technical difficulty in their usual application in hydrology. The choice of probability distributions for the calculation of extreme values in hydrology is, in most cases, made according to the ease of calculation of the estimated parameters and the explicit form of the inverse probability function. This article presents improved approximations and, in some cases, new approximations for the estimation with the method of ordinary moments and the method of linear moments, which are useful for the direct calculation of the parameters, because the errors in the approximate estimation are similar to the use of iterative numerical methods. Thirteen probability distributions of two and three parameters frequently used in hydrology are presented, for which parameter estimation was laborious. Thus, the approximate estimation of the parameters by the two methods is simple but also precise and easily applicable by hydrology researchers. The new and improved approximate forms presented in this article are the result of the research conducted within the Faculty of Hydrotechnics to update the Romanian normative standards in the hydrotechnical field.

Keywords

• probability distributions
• estimation parameters
• approximate form
• method of ordinary moments
• method of L-moments