Saddlepoint Approximations to the Density and the Distribution Functions of Linear Combinations of Ratios of Partial Sums |
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Authors: | Ehab F. Abd-Elfattah |
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Affiliation: | 1. Ain Shams University , Cairo , Egypt;2. University for Science and Technology , Ajman , United Arab Emirates ehab_abdelfatah@edu.asu.edu.eg |
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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. |
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Keywords: | Double saddlepoint approximation Linear combinations Linear combination of Dirichlet components Ratios of partial sums Saddlepoint approximation Uniform selected order statistics |
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