The Percentile Distributional Fitting tool (Figure TN.30) is another alternate way of fitting probability distributions. There are several related tools, and each has its own uses and advantages:
- Distributional Fitting (Percentiles)––using an alternate method of entry (percentiles and first/second moment combinations) to find the best-fitting parameters of a specified distribution without the need for having raw data. This method is suitable for use when there are insufficient data, only when percentiles and moments are available, or as a means to recover the entire distribution with only two or three data points but the distribution type needs to be assumed or known.
- Distributional Fitting (Single Variable)––using statistical methods to fit your raw data to all 45 distributions to find the best-fitting distribution and its input parameters. Multiple data points are required for a good fit, and the distribution type may or may not be known ahead of time.
- Distributional Fitting (Multiple Variables)––using statistical methods to fit your raw data on multiple variables at the same time. This method uses the same algorithms as the single variable fitting but incorporates a pairwise correlation matrix between the variables. Multiple data points are required for a good fit, and the distribution type may or may not be known ahead of time.
- Custom Distribution (Set Assumption)––using nonparametric resampling techniques to generate a custom distribution with the existing raw data and to simulate the distribution based on this empirical distribution. Fewer data points are required, and the distribution type is not known ahead of time.
Click on Risk Simulator | Analytical Tools | Distributional Fitting (Percentiles), choose the probability distribution and types of inputs you wish to use, enter the parameters, and click Run to obtain the results. Review the fitted R-square results and compare the empirical versus theoretical fitting results to determine if your distribution is a good fit.
Figure TN.30: Percentile Distributional Fitting Tool