The following articles and presentations provide important background for understanding and enabling effective use of the metalog distributions. It also includes references to additinoal quantile-parameterized distribution background material and other quantile-parameterized distributions.
"The Melalog Distributions" paper documents the motivation, literature review, definitions, mathematical derivations, and other background research for the equations and other materials implemented on this website. The typeset version, published in Decision Analysis in December 2016, is free to anyone with INFORMS/JSTOR access. To download it, click here. On the right is the pre-typeset version, which is free to everyone. To download it, click the icon.
"The Metalog Distributions" were explained in an invited lecture at Stanford University, Department of Management Science and Engineering, on February 28, 2017. To download a pdf of the PowerPoint slides, click the icon.
"Quantile Parameterized Distributions", published in Decision Analysis in September, 2011, provides an important theoretical and research-based background for parameterizing flexible continuous probability distributions with CDF data. The metalog distribution is the first published quantile-parameterized distribution (QPD) designed for broad and practical use. To download "Quantile Parameterized Distributions", click the icon.
"Quantile Function Methods For Decision Analysis" is a 2013 Stanford Ph.D. dissertation by Brad Powley. This work includes much of the same content as the co-authored "Quantile Parameterized Distributions" paper above but also significant additional contributions. These include a mathematically rigorous definition of QPDs, discussion of transformations of QPDs (which are themselves quantile-parameterized), and a novel theory of tail behavior which applies not only to QPDs but also to a wider range of continuous distributions. To download, click the icon.
"Johnson Quantile-Parameterized Distributions", authored by Chris Hadlock and Eric Bickel, was published in Decision Analysis in March, 2017. For bounded and semi-bounded distributions, Johnson Quantile-Parameterized Distributions (J-QPDs) offer quantile parameterization based on three assessed quantiles and a wide range of shape-flexibility -- similar to the three-paramater SPT semi-bounded and bounded metalog distributions. In contrast to the SPT metalogs, J-QPDs are maximally feasible.
The typeset version is free to anyone with INFORMS/JSTOR access. To download it, click here. On the right is the pre-typeset version, which is free to everyone. To download it, click the icon.
The J-QPD paper above includes equations for J-QPD CDF and quantile functions, but does not include equations for the J-QPD PDFs. The unpublished supplement on the right, "J-QPD Parameterizations," also authored by Hadlock and Bickel, provides the these PDF equations. Click on the icon to download it.