**8. Selection of probability distribution**

The probability distribution is a function for describing the probability of occurrence of a random event. Large amount of statistical information will be summarized in the distribution and its parameters by fitting a probability distribution on a set of hydrologic data. The most important and widely used methods for estimation of distribution parameters from data samples are method of moments, linear moments, and maximum likelihood which will be described more in next paragraph.

### **9. Method of moments**

The method of moments was first introduced by Pearson (1902). He found that the appropriate estimations of the parameters of a probability distribution are those which their moments match with corresponding sample moments in the best way. In this method, general formula for calculation of moments of order *r* of the distribution *f* (*x*) around the mean is:

$$
\mu^r = \int\_{\r^\infty}^{\r^\infty} \mathbf{x}^r f(\mathbf{x}) d\mathbf{x} \tag{5}
$$

The method of moments is describing the relation between moments and distribution param‐ eters. The most important moments around the mean are the mean, variance, skewness, and kurtosis, which are the one to four order moments, respectively.
