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<br />! The frequency factor in Equation 2 depends on the distribution selected. It is a <br />function of the specified exceedance probability and, in some cases, other population <br />parameters. The frequency factor function can be tabulated or expressed in <br />mathematical terms. <br /> <br />Kp = w - (2.515517 + 0.802853 w + 0.010328 w2) (12.5) (5) <br />(1 + 1.432788 w + ).189269 w2 + 0.001308 w3) <br /> <br />For example, normal-distribution frequency factors corresponding to the <br />exceedance probability p(O < p < 0.5) can be approximated with the following <br />equations (Abramowitz and Stegun, 1965): <br /> <br />(6) <br /> <br />in,which: <br />w = an intermediate variable, if p > 0.5, (1 - p) is used in equation 6, and the <br />computed value of Kp is multiplied by -1. <br /> <br />For the log-normal distribution Equation 2 is written as: <br /> <br />x =X + K S <br />p p <br /> <br />(7) <br /> <br />in which: <br />Xp =: <br />X <br />S <br />Kp =: <br /> <br />the logarithm of Qp' the desired quantile <br />= mean of logarfthm-s of sample <br />= standard deviation of logarithms of sample <br />the frequency factor <br /> <br />This frequency factor is the same as that used for the normal distribution. X and S are <br />computed with the following equation: <br /> <br />(8) <br /> <br />(9) <br /> <br />in which: <br />Q. <br />, <br />N <br /> <br />= observed peak annual discharge in year i <br />= number of years in sample <br /> <br />For the annual peak discharge values shown in Table 2, these values are as follows: <br /> <br />7-97 <br />