Expansions about the Gamma for the Distribution and Quantiles of a Standard Estimate

Christopher S. Withers and Saralees Nadarajah ()
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Christopher S. Withers: Industrial Research Limited
Saralees Nadarajah: University of Manchester

Methodology and Computing in Applied Probability, 2014, vol. 16, issue 3, 693-713

Abstract: Abstract We give expansions for the distribution, density, and quantiles of an estimate, building on results of Cornish, Fisher, Hill, Davis and the authors. The estimate is assumed to be non-lattice with the standard expansions for its cumulants. By expanding about a skew variable with matched skewness, one can drastically reduce the number of terms needed for a given level of accuracy. The building blocks generalize the Hermite polynomials. We demonstrate with expansions about the gamma.

Keywords: Bell polynomials; Gamma distribution; Normal distribution; 62E (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s11009-013-9328-9

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