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…
Archive for quantile distribution
A misleading title…
Posted in Books, R, Statistics, University life with tags bootstrap, fitting statistical distributions, generalized lambda distribution, GLDEX, International Statistical Review, John Tukey, Maple, Matlab, maximum likelihood estimation, quantile distribution, R on September 5, 2011 by xi'anQuantile distributions
Posted in Statistics, University life with tags ABC, quantile distribution on June 29, 2011 by xi'anKerrie 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
![\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)](https://s0.wp.com/latex.php?latex=%5Cqquad+A+%2B+B%5Cleft%5B1%2Bc%5Cdfrac%7B1-%5Cexp%5C%7B-g%5CPhi%28u%29%5C%7D%7D%7B1%2B%5Cexp%5C%7B-g%5CPhi%28u%29%5C%7D%7D%5Cright%5D%5C%7B1%2B%5CPhi%28u%29%5E2%5C%7D%5Ek%5CPhi%28u%29&bg=000000&fg=B0B0B0&s=0&c=20201002)
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.
