The Metalog Distributions

The Metalog Distributions

In economics, business, engineering, science and other fields, continuous uncertainties frequently arise that are not easily- or well-characterized by previously-named continuous probability distributions. Frequently, there is data available from measurements, assessments, derivations, simulations or other sources that characterize the range of an uncertainty. But the underlying process that generated this data is either unknown or fails to lend itself to convenient derivation of equations that appropriately characterize the probability density (PDF), cumulative (CDF) or quantile distribution functions.

The metalog distributions are a family of continuous univariate probability distributions that directly address this need. They can be used in 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. Consider their uses and benefits.  Also consider their applications over a wide range of fields and data sources. For additional perspective, read this
blog from a third-party user.

Many software implementations of metalog distributions are currently available. These include

free Excel workbooks programmed by the author of this website; SIPmath Tools from; Portfolio Navigator from SmartOrg; Analytica from Lumina Decision Systems; and an RMetalog function in R (the statistical programming language). See software implementations for details.  

This website is intended to complement and update "The Metalog Distributions", Decision Analysis, December, 2016.  The unabridged content of this paper is published on this website. Beyond this paper and current information about software implementations, this website offers the following:
  • Illustrative applications of the metalog distributions, including the fish biology, hydrology, and decision analysis examples in the paper -- and also including the input data on which the applications are based.
  • A more comprehensive set of closed-form moments of the unbounded metalog distribution than available in the paper.
  • An overview of notation and conventions used throughout the metalog system.
We hope you enjoy using the metalog distributions and that they help enhance your insight, effectiveness and success.