The Metalog Distributions

Uses & Benefits
Among the most flexible and easy-to-use continuous probability distributions, the metalogs have an increasingly wide range of practical uses:
  • Allow empirical data to "speak for itself" with highly-flexible continuous-distribution representations.
  • Get instant continuous-distribution representations for a wide range of 10/50/90 quantile assessments -- ideal for decision analysis applications.
  • Select among unbounded, semi-bounded, or bounded distributions according to your application
  • Skip time-consuming parameter estimation:  the input CDF (cumulative distribution function) data are themselves the parameters.

  • Use metalogs as convenient input distributions for Monte Carlo simulation: just generate a uniform random number (e.g. with the Excel RAND() function), and compute your sample using a simple closed-form algebraic equation.
  • Conveniently represent Monte Carlo simulation outputs as smooth, continuous probability distributions -- obviating the need for histograms or other artificially-lumpy output displays.
  • Use simple closed-form equations for quantile function (inverse CDF) and PDF (probability density function), which are directly programmable in Excel without macros and without advanced statistical packages or functions. 
Generally, metalogs are useful in a wide range of situations in which CDF data are known, and a simple, flexible, easy-to-use continuous probability distribution is needed to represent that data.