Laserfiche WebLink
<br />of Monte Carlo experiment by Wallis and others (1974). Their results show that the MSE of the logarithmic <br />station skew is a function of record length and population skew. For use in calculating W' this function <br />(MSEa) can be approximated with sufficient accuracy by the equation: <br /> <br />_ [A-B [logJO (N/JO)]] <br />MSEa - 10 <br />where A = -0.33 + 0.08 101 if 101 ~ 0.90, <br />-0.52 + 0.30 101 if 101 > 0.90, <br />B = 0.94 - 0.26 101 if 101 ~ 1.50, and <br />= 0.55 if 101 > 1.50. <br /> <br />(19) <br /> <br />in which 101 is the absolute value of the station skew coefficient (used as an estimate of population skew <br />coefficient) and N is the record length in years. If the historic adjustment (Bulletin 17B, Appendix 6) has <br />been applied, the historically adjusted skew coefficieut, 0, and historic period, H, are to be used for 0 and <br />N, respectively, in equation 19. Application of equation 19 to stations with absolute skew coefficients <br />(logs) greater than 2 causes decreasing weight to be given to the station coefficient when the period of <br />record increases. Application of equation 18 also may give improper weight to the generalized skew <br />coefficient if the generalized and station skew coefficients differ by more than 0.5. In these situations, an <br />examination of the data and the flood-producing characteristics of the watershed should be made and <br />possibly greater weight gi ven to the station skew coefficient. <br /> <br />Expected Probability Adjustment <br /> <br />The final steps in the Bulletin 17B analysis, as implemented in program PEAKFQ, are to compute the <br />so-called expected-probability frequency curve and a set of upper and lower confidence limits. These <br />computations are optional and are intended primarily as an aid to the interpretation of the principal Bulletin <br />17B-estimated frequency curve given by Q above. <br />The expected probability concept deals with the following problem. A sample of size n will be drawn <br />from a normal population (of flood logarithms), and the flood having exceedance probability p will be <br />estimated by the quantity X + k (S), in which X and S are the ordinary sample mean and standard <br />p <br />deviation and k is the standard normal frequency factor for probability p. Because it is computed from a <br />p <br />random sample, the estimate X + kp (S) is a random variable, which usually will differ from the true <br />p-probability flood. Thus one is led to ask how the probability of another flood exceeding the estimate <br />X + k (S) compares with the nominal probability p. For a normal population one has: <br />p <br /> <br />x-X, ~ <br />P{X>X+ (k )S} = P{-S >k} = P{t l>k [n/(n+ 1)] } <br />p p n- p <br /> <br />(20) <br /> <br />where tn ~ 1 is Student's t with n-l degrees of freedom. This probability has come to be known as the <br />"expected probability" (Beard, 1960; Interagency Advisory Committee on Water Data, 1982, Appendix <br /> <br />PEAKFQ <br /> <br />12 <br /> <br />DRAFT .1/30/98 <br />