Saddlepoint Approximations to the Density and the Distribution Functions of Linear Combinations of Ratios of Partial Sums
Abd-elfattah, Ehab;
Abstract
A class of ratios of partial sums, including Normal, Weibull, Gamma, and Exponential distributions, is considered. The distribution of a linear combination of ratios of partial sums from this class is characterized by the distribution of a linear combination of Dirichlet components. This article presents two saddlepoint approaches to calculate the density and the distribution function for such a class of linear combinations. A simulation study is conducted to assess the performance of the saddlepoint methods and shows the great accuracy of the approximations over the usual asymptotic approximation. Applications of the presented approximations in statistical inferences are discussed. © 2013 Copyright Taylor and Francis Group, LLC.
Other data
Title | Saddlepoint Approximations to the Density and the Distribution Functions of Linear Combinations of Ratios of Partial Sums | Authors | Abd-elfattah, Ehab | Issue Date | 2013 | Journal | Communications in Statistics - Theory and Methods | DOI | 23 https://api.elsevier.com/content/abstract/scopus_id/84887455055 4185 42 10.1080/03610926.2011.633731 |
Scopus ID | 2-s2.0-84887455055 |
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