The Distribution Fitting analysis allows the user to analyze the inherent uncertainty associated with probability distribution | fitting method combinations when using nearly any type of data. Nineteen different analytical distributions and three different fitting methods can be used in combination with regular interval, irregular interval, and/or paired data (for example, count vs. time of concentration). The previously mentioned data filtering is integrated within the analysis. Additionally, confidence limits and expected probability curves can be computed for any analytical distribution | fitting method combination.

Create a new Distribution Fitting Analysis and Filter Data

  • Create a new Distribution Fitting analysis and name it "Hawley_DFA".
  • Select the Hawley precipitation data set within the Data Set drop down menu.

The data set will be named "Hawley Daily Precipitation".

  • On the Data tab, ensure that Precipitation is selected within the Parameter Type drop down.
  • Click on the Filter Data button.
  • Within the Filter editor, move to the Peaks tab and click the Filter Data by Peaks Over Threshold (Partial Duration) check box.
  • Enter a Minimum Threshold of 1 and a delete the contents of the Duration of time between peaks entry field.
  • Click OK to close the Filter editor. 
  • Choose the XY radio button below the plot.
  • The Data tab should appear similar to Figure 1.

Figure 1. Hawley_DFA Data Tab

Visualize Multiple Distributions

  • Move to the Analysis tab.
  • Click the radio button to Display All Distributions.
  • Within the Distribution Fitting Methods panel, select the L-Moments (LM) checkbox, as shown in Figure 2. This will switch the fitting method from standard product moments to linear moments.

Figure 2. Enabling the Linear Moments Fitting Method

  • Within the table of distributions and fitting methods, find the Generalized Pareto (LM) model.
  • Click on the left-most check box in this row to display the median curve for the selected model, as shown in Figure 3.

Figure 3. Hawley_DFA Analysis Tab

  • Try multiple distribution and fitting method choices. Also, try changing the Plot Type to PDF, PP Plot, QQ Plot, and CDF-Plotting Position.

It is important to note that many of the analytical probably distributions within the Distribution Fitting Analysis are meant for block maxima (e.g., annual maximum series) and are not appropriate for partial duration series where there may be 0 to many events each year. When selecting a probability distribution, consider the data that is being modeled and do not solely rely on goodness of fit metrics.

Additional tutorials on partial duration series can be found here: Partial Duration Workshop 2023.

Accept a Distribution and Visualize the Results

  • Once you have determined an acceptable distribution and fitting method, click the corresponding radio button within the Accept Distribution column. This will compute the confidence limits and expected probability curve (if they weren’t already computed).
  • Move to the Results tab. Within this tab, you will find statistics and parameters related to the original data, filtered data, selected distribution and fitting method, selected goodness of fit method, as well as the computed frequency curves, as shown in Figure 4.

Figure 4. Hawley_DFA Results Tab

  • Click the View Report button to open the report.
  • Within the report window, take note of the expanded information that can only be found within the report file. When you are finished scrolling through the report, close the window by clicking the "X" button in the upper right corner of the window.

Download the final project files here: Intro_to_SSP.zip