Handbook of Statistical Distributions with Applications

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The second edition (1st in 2006) of the Handbook of Statistical Distributions with Applications is a reference book based on Prof. Krishnamoorthy’s interests in theoretical & applied topics concerning distributions such as classical frequentist and fiducial inference. The book seeks to be a non-exhaustive guide covering seven discrete, twenty continuous and five non-parametric distributions/tests. Starting with an excellent summary of general theoretical (e.g. defining unbiased tests) and applied (e.g. MOVER for “accurate approximate” CI) results, the structure of each chapter presents algebraic properties & then illustrates the distribution with basic B&W graphs. All examples use the StatCalc program (available from the author’s website), with data from a variety of illustrative sources (e.g. medical, manufacturing), and more detail (e.g. on confidence, prediction & tolerance intervals) is given to the most popular distributions (i.e. Normal). Chapters finish with useful properties, relationships to other distributions and computational considerations. The update broadly concerns extending the free Windows StatCalc(3.0) software by including some additional results on different interval estimation for some distributions (e.g. Binomial) and results for intervals and tests for given sample sizes (e.g. Poisson). This software gives explicit additional control over many aspects of distributions, and useful extra summaries (e.g. moments, point estimation, different types of CI – approximate vs fiducial) above those available in comparable software, although it would be less useful than other software for the purpose of sample size estimation. R functions (website file) have been referred to in the text when addressing topics beyond the scope of StatCalc (e.g. calculating MLEs). The main value above being just a reference manual providing a through grounding in theoretical results, is in presenting the author’s description of some recent alternative methods for CI estimation (e.g. with reference to Newcombe’s approaches) and discussions of their comparisons (e.g. speed of calculation, relative merits). Additionally, the notes on implementation of distributions will be valuable to users seeking efficient ways to model or find the inverse of a wide range of distributions, although there is sometimes too much R code provided in print. In summary, this is a fairly comprehensive reference guide, well organised & with an authoritative style and many examples. Weight is given to the most popular distributions, and calculations are implemented in StatCalc. It deals with the practicalities of the uses of distributions which are directly relevant for classical analysts (i.e. CI estimation) and indirectly to others (e.g. applied Bayesian MCMC modelling).

38 Economics, 4905 Statistics, 3802 Econometrics, 49 Mathematical Sciences
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Journal of the Royal Statistical Society Series A: Statistics in Society
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Oxford University Press (OUP)
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