The Metalog Distributions

Equations

For user convenience, the metalog equations implemented in the metalog Excel workbooks are briefly documented in this section. Before examining them, you may wish to review the notation and conventions used throughout the metalog system. For more complete documentation, see The Metalog Distributions. Click on a link below to see the relevant equations.
Each set of equations includes the metalog quantile function (inverse CDF), the metalog PDF, and also a feasibility condition that must be satisfied in order for these equations to yield a valid probability distribution.  Generally, the feasibility condition is that the PDF is strictly positive for all cumulative-probabilities y in the open interval (0,1). If this condition is not satisfied, the associated metalog distribution does not exist for the particular input data and number of terms (n) under consideration. For more information, see The Metalog Distributions, Section 3, Equations (5) and (10).