For each of the assigned distributions, determine (1) the return period for a discharge of 20 m'ls and (2) the discharge with a return period of 100 years.

Problem

Array the discharges for River 1 and analyze the data as follows: (1) Determine the return period r,, and probability p associated with each value. (2) Calculate the arithmetic mean and standard deviation and the mean, standard deviation, and coefficient of skew for the logs of the discharges as required for the assigned portions of this problem. (3) Plot the discharges on normal probability paper and compare the results with the straight line of best fit based on the normal distribution. (4) Plot the discharges on lognormal paper and compare the results with the straight line of best fit based on the lognormal distribution. (5) Compare the plotted data in part (4) with the log Pearson Type 111 distribution by plotting this distribution on the graph using the calculated value of skew. (6) Plot the discharges on extreme value paper and compare the results with the straight line of best fit based on the extreme value distribution. (7) Which distribution best represents this data set?