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<br />! assumptions: <br /> <br />4.1.1. The streamflow-probability relationship of the parent population can <br />be represented with a selected distribution. The moments (derivatives) of the <br />distribution equation can be determined with calculus. One moment is determined for <br />each parameter of the distribution. The resulting expressions are equations in terms of <br />the parameters of the distribution. <br /> <br />4.1.2. Moments of a sample of the parent population can be computed <br />numerically. The first moment is the mean of the sample. The second moment is the <br />variance. The third moment is the sample skew. Other moments can be found if the <br />distribution selected has more than three parameters. <br /> <br />4.1.3. The numerical moments of the sample are the best estimates of the <br />moments of the parent population. This assumption permits development of a set of <br />simultaneous equations. The distribution parameters are unknown in the equations. <br />Solution yields estimates of the parameters. <br /> <br />When the parameters of the distribution are estimated, the inverse <br />distribution defines the quantiles of the frequency curve. Chow (1 951) showed that <br />with the method-of-moments estimates, many inverse distributions commonly used in <br />hydrologic engineering could be written in the following general form: <br /> <br />Op = a + KpS <br /> <br />(2) <br /> <br />in which: <br /> <br />O. = the quantile with specified exceedance propability p <br />a = the sample mean <br />S = the sample standard deviation <br />K. = a frequency factor <br /> <br />The sample mean and standard deviation are computed with the following equations: <br /> <br />(3) <br /> <br />(4) <br /> <br />in which; <br /> <br />0; = observed event i <br />N = number of events in sample <br /> <br />7-96 <br />