The Metalog Distributions

Applications & Data

Metalog distributions can be useful across a wide range of fields and purposes -- for most any situation in which CDF data is known and a flexible, simple, and easy-to-use continuous probability distribution is needed to represent that data. Purposes may range from simply displaying a probability density function (PDF) that appropriately represents CDF data; quickly developing continuous distributions that correspond to 10%, 50%, and 90% quantile assessments in decision analysis; setting up a convenient continuous Monte Carlo simulation based on discrete data; and enabling a large set of empirical or simulation data "to speak for itself" regarding its probabilistic shape and other characteristics.

To facilitate "hands on" metalog experience and future research, we offer a range of input data sets in Excel. These data sets may be copied and pasted into our Excel workbooks.  Instant results will appear.  One can also see how changing this data would change the results. The workbook on the right is in ".xlsx" format (Excel 2007 or later) and contains no macros, named ranges, or references to external workbooks. Thus, it can be safely copied, pasted, and otherwise ported into other workbooks or environments. Click the icon to download.

Example Metalog Input Data
Contents of this workbook include the following (references in parentheses cite context and further information in The Metalog Distributions):
  • Fish biology data for the weight of 3,474 steelhead trout which were caught and released in 2006-2010 (Section 6.1.1, Figure 10 and Section 6.3, Figure 15).
  • Hydrology data for the gauge height of the Williamson River, OR, 1920-2014 (Section 6.1.2, Figure 11 and Section 6.3, Figure 16).
  • 10%, 50%, and 90% input data for Assets 1 and 2 of the a bidding decision analysis (p. 50, Table 9 and Figure 14).
  • Simulation results data for a bidding decision analysis (Section 6.2.2 and Figures 12-13).
  • Data from traditional distributions that may be used to observe and test the accuracy of their metalog approximations.  These include the normal, extreme value, student t, lognormal, gamma, beta, and triangular (Section 5, Tables 5-8 and Figures 8-9).
  • Example data sets of m = 10,000 input data that may be used to observe recalculation performance with large data sets.
For all of the above, indication of which Excel Workbook is most appropriate to use.  Users are also encouraged to use these workbooks to enter, learn about, and experiment with their own data.