Using the results of Examples 1 and 2, write the probability density function assuming a normal distribution and a log-normal distribution for the annual peak discharges (Qi) of the Meherrin River at Emporia, Virginia.
Consider the Meherrin River discharges given in Example 1. Compute the mean, standard deviation, and skew coefficient of the logarithms of the observed discharges.
First, the logarithms of the Q’s are obtained and tabulated in column 6 of Table 12.1. Then calculations are performed in tabular form as in Example 1. However, in this case, Equations 1, 2, and 3 are used where log Qi has been substituted for the log xi terms. Thus,
Note that the mean flow for the log-transformed data set can be found by taking the antilog (sometimes referred to as the inverse log):
which is much lower than the arithmetic mean.