For fitting multiple variables, the process is fairly similar to fitting individual variables. However, the data should be arranged in columns (i.e., each variable is arranged as a column) and all the variables are fitted. The same analysis is performed when fitting multiple variables as when single variables are fitted. The difference here is that only the final report will be generated and you do not get to review each variable’s distributional rankings. If the rankings are important, run the single variable fitting procedure instead, on one variable at a time.

  • Open a spreadsheet with existing data for fitting (e.g., use the Risk Simulator | Example Models | 06 Data Fitting).
  • Select the data you wish to fit (data should be in multiple columns with multiple rows).
  • Select Risk Simulator | Analytical Tools | Distributional Fitting (Multi-Variable).
  • Review the data, choose the types of distributions you want to fit to, and click OK.

Notice that the statistical ranking methods used in the distributional fitting routines in the examples above are the chi-square test and Kolmogorov–Smirnov test (other distributional fitting methods are discussed in the next section). The former is used to test discrete distributions and the latter, continuous distributions. Briefly, a hypothesis test coupled with the maximum likelihood procedure with an internal optimization routine is used to find the best-fitting parameters on each distribution tested and the results are ranked from the best fit to the worst fit. There are other distributional fitting tests such as the Shapiro-Wilks, etc. However, these tests are very sensitive parametric tests and are highly inappropriate in Monte Carlo risk simulation distribution-fitting routines when different distributions are being tested. Due to their parametric requirements, these tests are most suited for testing normal distributions and distributions with normal-like behaviors (e.g., binomial distribution with a high number of trials and symmetrical probabilities) and will provide less accurate results when performed on non-normal distributions. Take great care when using such parametric tests. The Kolmogorov–Smirnov and chi-square tests employed in Risk Simulator are nonparametric and semiparametric in nature and are better suited for fitting normal and non-normal distributions. Additional distributional fitting methods are discussed next.

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