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3.9.1 Distribution Selection: Practical Considerations Many different probability distributions have been proposed for application to hydrologic data. Some of them were proposed because the underlying concept of the distribution matched the goal of hydrologic frequency analysis. For ex­ample, the extremal distributions discussed in Sec. 2.6.4 have very favorable properties for hydrologic frequency analysis. Ang and […]

Consider Example 3.2 in which the annual maximum flood peak discharges over a 15-year period on the Boneyard Creek at Urbana, Illinois, were analyzed. Suppose that the annual maximum floods follow the Gumbel distribution. The estimated 25-year flood peak discharge is 656 ft3/s. It is not difficult to imag­ine that if one had a second […]

Based on a given sample of finite observations, procedures are needed to help identify the underlying distribution from which the random samples are drawn. Several statistical goodness-of-fit procedures have been developed (D’Agostino and Stephens, 1986). The insensitivity to the tail portion of the distribution of the conventional chi-square test and Kolmogorov-Smirnov test has been well […]

For a chosen distributional model, its shape and position are completely defined by the associated parameters. By referring to Eq. (3.5), determination of the quantile also requires knowing the values of the parameters в. There are several methods for estimating the parameters of a distribution model on the basis of available data. In frequency analysis, […]

An alternative to the graphic technique is to estimate the statistical parameters of a distribution from the sample data (refer to Sec. 3.6). Then the distribution model can be used to solve for the variate value corresponding to any desired return period or probability as in which F-1(e) is the inverse cumulative distribution function with […]

Once the data series is identified and ranked and the plotting position is calcu­lated, a graph of magnitude x versus probability [P(X > x), P(X < x), or T] can be plotted and a distribution fitted graphically. To facilitate this procedure, it is common to use some specially designed probability graph paper rather than linear […]

As stated previously, the objective of frequency analysis is to fit geophysical data to a probability distribution so that a relationship between the event magnitude and its exceedance probability can be established. The first step in the procedure is to determine the type of data series (i. e., event magnitude) to be used. In order […]

Hydrosystems engineers have been using the concept of the return period (or sometimes called recurrence interval) as a substitute for probability because it gives some physical interpretation to the probability. The return period for a given event is defined as the period of time on the long-term average at which a given event is equaled […]

The first step in the frequency-analysis process is to identify the set of data or sample to be studied. The sample is called a data series because many events of interest occur in a time sequence, and time is a useful frame of reference. The events are continuous, and thus their complete description as a […]

One of the basic questions in many hydrosystems infrastructural designs that an engineer must answer is, “What should be the capacity or size of a system?” The planning goal is not to eliminate all hydro-hazards but to reduce the fre­quency of their occurrences and thus the resulting damage. If such planning is to be correct, […]