Probability distributions for hydrologic variables

Pearson type III distribution

Famous statistician Carl Pearson developed a whole system consisting of seven types of distributions. The Pearson type III distribution is sometimes called three-parameter gamma distribution, since it can be obtained from the two-parameter gamma distribution by introducing so-called location parameter c:

Parameter c is also the lower bound forthis distribution (x c). The Pearson type III distribution is very flexible since it has three parameters which can produce a wide variety of shapes of density function. Parameter a is governing the skewness of the distribution, and when it tends to infinity, the Pearson type III distribution becomes normal distribution.

Similar to normal distribution, cumulative distribution function for the Pearson type III distribution is not available in closed form. Calculation of this distribution is usually performed via frequency factor, defined as:

Frequency factor for the Pearson type III distribution depends on probability of non-exceedance F and skewness coefficient Cs. Its values can be found in statistical tables.

The Pearson type III distribution is frequently used for annual maximum floods.

 

Log-Pearson type III distribution

Random variable X follows log-Pearson type III distribution if random variable Y†=†ln†X (or Y†=†log X) follows the Pearson type III distribution. Log-normal distribution is a special case of the log-Pearson type III distribution when skewness coefficient of logarithmic data is equal to 0 (Csy = 0).

This distribution is mostly used for annual maximum floods. In the USA, it is a standard distribution for flood frequency analysis.


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