An iterative procedure for the estimation of the parameters of stable laws

Koutrouvelis, Ioannis A.

doi:10.1080/03610918108812189

Cited by 179 publications

(127 citation statements)

References 6 publications

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“…Koutrouvelis noted that (2.2) implies that Koutrouvelis (1980Koutrouvelis ( , 1981 and Kogon and Williams (1998) have studied refinements of the estimation procedure above and have also done simulation experiments to demonstrate that this approach works well and is quite efficient, provided that the λ-values are carefully selected and the data are suitably normalized. Koutrouvelis (1980) indicates how to select appropriate λ-values.…”

Section: The Koutrouvelis Methodsmentioning

confidence: 99%

Is the Pareto–Lévy law a good representation of income distributions?

Dagsvik

Jia

Vatne³

et al. 2011

Empir Econ

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract Mandelbrot (1960) proposed using the so-called Pareto-Lévy class of distributions as a framework for representing income distributions. We argue in this paper that the Pareto-Lévy distribution is an interesting candidate for representing income distribution because its parameters are easy to interpret and it satisfies a specific invariance-under-aggregation property. We also demonstrate that the Gini coefficient can be expressed as a simple formula of the parameters of the Pareto-Lévy distribution. We subsequently use Terms of use: Documents in EconStor may

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Section: The Koutrouvelis Methodsmentioning

confidence: 99%

Is the Pareto–Lévy law a good representation of income distributions?

Dagsvik

Jia

Vatne³

et al. 2011

Empir Econ

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“…Fama and Roll [17], and later [2,3] used the truncated sample mean for δ and sample quantiles for γ, while [4,5] proposed search methods for the initial estimates of δ and γ. However, we propose scaling by sample median, i.e., apply cumulant estimation procedure on the reduced (by sample median) data.…”

Section: Proof From Euler's Formula We Haveψmentioning

confidence: 99%

“…For studies on parameter estimation of stable laws based on empirical characteristic function, we refer, for example, to [2][3][4][5][6][7][8]12,13]. For a sample X 1 , .…”

Section: Definitionmentioning

confidence: 99%

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Parameter Estimation in Stable Law

Krutto

2016

Risks

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“…A widely used method for estimating a stable distribution is based on the ECF. References include Press (1972), Paulson et al (1975), Arad (1980), Koutrouvelis (1980Koutrouvelis ( , 1981, Feuerverger and McDunnough (1981a), Brockwell and Brown (1981), Paulson and Delehanty (1985) and Kogon and Williams (1998).…”

Section: Stable Distributionmentioning

confidence: 99%

Empirical Characteristic Function Estimation and its Applications

2003

SSRN Journal

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This paper reviews the method of model-fitting via the empirical characteristic function. The advantage of using this procedure is that one can avoid difficulties inherent in calculating or maximizing the likelihood function. Thus it is a desirable estimation method when the maximum likelihood approach encounters difficulties but the characteristic function has a tractable expression. The basic idea of the empirical characteristic function method is to match the characteristic function derived from the model and the empirical characteristic function obtained from data. Ideas are illustrated by using the methodology to estimate a diffusion model that includes a self-exciting jump component. A Monte Carlo study shows that the finite sample performance of the proposed procedure offers an improvement over a GMM procedure. An application using over 72 years of DJIA daily returns reveals evidence of jump clustering.

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An iterative procedure for the estimation of the parameters of stable laws

Cited by 179 publications

References 6 publications

Is the Pareto–Lévy law a good representation of income distributions?

Is the Pareto–Lévy law a good representation of income distributions?

Parameter Estimation in Stable Law

Empirical Characteristic Function Estimation and its Applications

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