Part II-8-5-c. There is no strong theoretical reason for preferring one distribution function over another. The

single sample cannot be expected to fit the true distribution function exactly, especially for the few largest

events. For some processes, such as water levels, one particular distribution function is generally accepted

for all applications. For other processes, such as significant wave heights, a best-fitting distribution function

is often chosen from among several candidates.

(b) Typically, extreme data values are sorted into descending order. A nonexceedance probability must

be assigned to each extreme data value. These *plotting positions *should be chosen so that the distribution

function can be accurately estimated. Figure II-8-5 gives the commonly used traditional plotting position

formula. The figure also gives formulas developed to remove bias and minimize *rms *errors when fitting to

specific distribution functions (Goda 1988, Goda and Kobune 1990).

(3) Approaches to estimating parameters. The following approaches can be used to determine parameters

for each candidate distribution function:

(a) Graphical approach. Traditionally, the goodness of fit was determined visually by plotting the data

along with candidate distribution functions. By scaling the plotting axes to make a candidate distribution

appear as a straight line, the parameters of a visually optimum distribution function can more easily be

determined.

(b) Computational approach. An automated computational approach is more objective (though not

necessarily more accurate) and often easier to apply than the relatively tedious graphical approach. Three

alternatives are the least squares method, the maximum likelihood method, and the method of moments. The

least squares method is simplest and, with two-parameter distribution functions, it is often used. It is included

in the ACES software package. One caution with this approach is that it is sensitive to even one or two

extreme points that deviate greatly from the general trend of the data (*outliers*). The maximum likelihood

method has the advantage of being less likely to produce erratic results when the data contain outliers or differ

somewhat from the distribution function (Mathiesen et al. 1994). More information on computational

approaches is also available from Goda (1988, 1990). Regardless of the method used, it is

II-8-10

Hydrodynamic Analysis and Design Conditions

Integrated Publishing, Inc. |