منابع مشابه
The Refined Positive Definite and Unimodal Regions for the Gram-Charlier and Edgeworth Series Expansion
Gram-Charlier and Edgeworth Series Expansions are used in the field of statistics to approximate probability density functions. The expansions have proven useful but have experienced limitations due to the values of the moments that admit a proper probability density function. An alternative approach in developing the boundary conditions for the boundary of the positive region for both series e...
متن کاملGram Charlier Expansion for Time Varying Multiserver Queues with Abandonment
In this paper, we introduce a new approximation for estimating the dynamics of multiserver queues with abandonment. The approximation involves a four-dimensional dynamical system that uses the skewness and kurtosis of the queueing distribution via the Gram Charlier expansion. We show that the additional information captured in the skewness and kurtosis allows us to estimate the dynamics of the ...
متن کاملApplication of the Gram-Charlier Approximation for Option Valuation
The Hermite polynomials form the basis of a Hilbert space and may be used to get an expansion of the probability density function. Usually, this series is called Gram-Charlier. For practical purposes, only the first few terms of this expansion are taken into consideration. The resulting truncated series may be viewed as the normal probability density function multiplied by a polynomial that acc...
متن کاملThe Gram-Charlier A Series based Extended Rule-of-Thumb for Bandwidth Selection in Univariate and Multivariate Kernel Density Estimations
The article derives a novel Gram-Charlier A (GCA) Series based Extended Rule-of-Thumb (ExROT) for bandwidth selection in Kernel Density Estimation (KDE). There are existing various bandwidth selection rules achieving minimization of the Asymptotic Mean Integrated Square Error (AMISE) between the estimated probability density function (PDF) and the actual PDF. The rules differ in a way to estima...
متن کاملFitting German into N-Gram Language Models
We report on a series of experiments addressing the fact that German is less suited than English for word-based n-gram language models. Several systems were trained at different vocabulary sizes using various sets of lexical units. They were evaluated against a newly created corpus of German and Austrian broadcast news.
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1943
ISSN: 0003-4851
DOI: 10.1214/aoms/1177731459