Log Pearson Type III Distribution

The Pearson Type III, or Gamma, distribution is used to calculate the frequency of maxima events when the distribution of all events (both big and small) is log-normally distributed.  Events will be log-normally distributed when they are the product of a large number of independent random variables.  In hydrologic applications, the log-normal distribution has been found to reasonably describe such variables as the depth of precipitation of individual storms and annual peak discharges.  This distribution was first used to describe the probability of annual peak discharges by H. Alden Foster in 1924 ("Theoretical frequency curves and their application to engineering problems", Transactions of the American Society of Civil Engineers, 87:142-73).  Today, the application of this distribution to quantify the recurrence interval of large peak annual discharges is recommended by the U.S. Interagency Advisory Committee on Water Data ("Guidelines for Determining Flood Flow Frequency", Bulletin 17B of the Hydrology Committee, U.S. Geological Survey, Reston, VA).  It is the default distribution used by the U.S. Geological Survey for flood studies.