Download page Task 2. Fit Distributions using the Distribution Fitting Analysis in HEC-SSP.
Task 2. Fit Distributions using the Distribution Fitting Analysis in HEC-SSP
Fit the Generalized Pareto Distribution to the Partial Duration Series
We will select PDS5 to use in this task. If time allows at the end of this workshop, you can repeat this task with a different partial duration series.
Create a new Distribution Fitting analysis by right clicking on the Distribution Fitting folder in the Study Explorer and selecting New or by selecting Analysis | New | Distribution Fitting Analysis from the top ribbon.
Enter "AppleRiver_PDS5" as the Name.
Choose "Apple River-Hanover, IL-FLOW-PDS5" as the Data Set.
Instead of filtering and creating new data sets for the various partial duration series, you could click the Filter Data button within the Distribution Fitting Analysis to apply the same filtering criteria.
Select the Analysis tab.
In the Distribution Filter panel, select the Display All Distributions radio button.
Select the L-Moments (LM)checkbox in the Distribution Fitting Method panel. Uncheck the boxes for the other two distribution fitting methods.
Select the Generalized Pareto (LM) distribution and click the Accept Distribution radio button in that row.
On the Analysis tab, look at the Kolmogorov-Smirnov, Chi-Square, and Anderson Darling Tests Statistics.
In the lower right, select the PP Plot radio button to view the P-P plot. Next, select the QQ Plot radio button to view the Q-Q plot.
View the Results tab.
When you're done, close the distribution fitting analysis by selecting OK.
QUESTION 3: Why is the Generalized Pareto distribution the appropriate analytical probability distribution for a partial duration series?
The Generalized Pareto distribution is used to characterize the probabilities of exceedances over a substantially high threshold. A partial duration series is comprised of events exceeding a threshold.
Fit the Generalized Extreme Value Distribution to the Annual Maximum Series
Create a new Distribution Fitting analysis by right clicking on the Distribution Fitting folder in the Study Explorer and selecting New or by selecting Analysis | New | Distribution Fitting Analysis from the top ribbon.
Enter "AppleRiver_AMS" as the Name.
Choose "Apple River-Hanover, IL-FLOW-AMS" as the Data Set.
Select the Analysis tab.
In the Distribution Filter panel, select the Display All Distributions radio button.
Select the L-Moments (LM) checkbox in the Distribution Fitting Method panel. Uncheck the boxes for the other two distribution fitting methods.
Select the Generalized Extreme Value (LM) distribution and click the Accept Distribution radio button in that row.
View the Results tab. Look at the Kolmogorov-Smirnov, Chi-Square, and Anderson Darling Tests Statistics.
When you're done, close the distribution fitting analysis by selecting OK.
QUESTION 4: Which distribution has the smallest Kolmogorov-Smirnov Test Statistic for this data set? Is this distribution an appropriate analytical probability distribution to use for an annual maximum series? Why or why not?
The Generalized Pareto distribution has the lowest K-S test statistic. However, the Generalized Pareto distribution is not an appropriate analytical probability distribution to model an annual maximum series. Events comprising an annual maximum series do not necessarily exceed a threshold; they are simply the largest in a year-long period.
