## Archive for quantile distribution

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , on September 5, 2011 by xi'an

When I received this book, Handbook of fitting statistical distributions with R, by Z. Karian and E.J. Dudewicz,  from/for the Short Book Reviews section of the International Statistical Review, I was obviously impressed by its size (around 1700 pages and 3 kilos…). From briefly glancing at the table of contents, and the list of standard distributions appearing as subsections of the first chapters, I thought that the authors were covering different estimation/fitting techniques for most of the standard distributions. After taking a closer look at the book, I think the cover is misleading in several aspects: this is not a handbook (a.k.a. a reference book), it does not cover standard statistical distributions, the R input is marginal, and the authors only wrote part of the book, since about half of the chapters are written by other authors…

## Quantile distributions

Posted in Statistics, University life with tags , on June 29, 2011 by xi'an

Kerrie Mengersen, who is visiting CREST and Dauphine this month, showed me a 2009 paper she had published in Statistics and Computing along with D. Allingham and R. King on an application of ABC to quantile distributions. Those distributions are defined by a closed-form quantile function, which makes them easy to simulate by a simple uniform inversion, and a mostly unavailable density function, which makes any approach but ABC difficult or at least costly to implement. For instance, the g-and-k distribution is given by

$Q(u;A,B,g,k) = \qquad\qquad\qquad$

$\qquad A + B\left[1+c\dfrac{1-\exp\{-g\Phi(u)\}}{1+\exp\{-g\Phi(u)\}}\right]\{1+\Phi(u)^2\}^k\Phi(u)$

hence can be simulated by a single call to a normal simulation. This is therefore a good benchmark for realistic albeit simple examples to use in ABC calibration and we are currently experimenting with it.