Laserfiche WebLink
<br />in which n is the sample size. If the underlying population were normally distributed, and if j{ and s were <br />the ordinary sample mean and standard deviation, then the random variable on the left-hand side of the <br />inequality would have the noncentral t distribution with n-I degrees of freedom and noncentrality <br />parameter Jll (ky,p) . If the underlying population becomes less skewed, if the sample size increases, and <br />if the population skew coefficient, y, could be replaced by the Bulletin 17B estimated skew coefficient, <br />Gw' then one might hope the variate would have approximately the noncentral-t distribution. Building <br />upon this foundation, one obtains: <br /> <br />Jll (K) = tn -1' Jll(kG ), (I - a) <br />w,p <br /> <br />(24) <br /> <br />which is the noncentral-t value with exceedance probability I-a. A standard large-sample approximation <br />for the noncentral-t distribution then yields the result: <br /> <br />K= <br /> <br />( ) k (I _ a) (2 2) 0.5 <br />kGw'p + Jll {I + nk Gw,p-k(l_a) n(n-I)} <br />2 <br />{I - k (1- a/2 (n - I) } <br /> <br />(25) <br /> <br />in which k (1- a) is the standard normal deviate with exceedance probability (I - a) and Gw is the <br />Bulletin 17B estimated skew coefficient. As stated above, an a-value near unity yields upper confidence <br />limits whereas a value near zero yields lower limits. This result is equivalent to that in the Bulletin 17B <br />guidelines. <br /> <br />PEAKFQ <br /> <br />14 <br /> <br />DRAFT - 1/30/98 <br />