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Author Maesono, Yoshihiko ♦ Penev, Spiridon I.
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Cornish-fisher Expansion ♦ Saddlepoint Approximation ♦ Order Relation ♦ Lugannani-rice Approximation ♦ Many Numerical Example ♦ Inverse Problem ♦ Third Order Coincides ♦ General Setting ♦ Lugannani-rice Formula ♦ Quantile Evaluation ♦ Third Order Edgeworth Expansion ♦ Explicit Approximation ♦ General Normalised Statistic Behaves ♦ Cornish-fisher Formula ♦ Small Sample ♦ Cumulative Distribution Function
Abstract In many numerical examples it has been demonstrated that the saddlepoint approximation for the cumulative distribution function of a general normalised statistic behaves better in comparison with the third order Edgeworth expansion. The effect is especially pronounced in the tails. Here we are dealing with the inverse problem of quantile evaluation. The inversion of the Lugannani-Rice approximation is compared with the Cornish-Fisher expansion both theoretically and numerically. We show in a very general setting that the expansion of the inversion of the Lugannani-Rice approximation up to third order coincides with the Cornish-Fisher expansion. Based on this, an explanation of the superiority of the former in comparison with the latter in the tails and for small samples is given. An explicit approximation of the inversion of the Lugannani-Rice formula is suggested that utilizes the information in the cumulant generating function and improves upon the Cornish-Fisher formula.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study