Regression-Type Estimation of the Parameters of Stable Laws

Koutrouvelis, Ioannis A.

doi:10.2307/2287182

Cited by 133 publications

(127 citation statements)

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“…As indicated in Section 4.2, it is possible to obtain an informal test of stability by plotting the empirical counterpart of the left-hand side of (4.1) against ln λ . This plot is displayed in Figure 1, where the data are scaled as suggested in Koutrouvelis (1980). Figure 1 shows that the plot is fairly linear up to ln 0.7 λ ≈…”

Section: Results For Norwaymentioning

confidence: 96%

“…The method proposed by Koutrouvelis (1980) is based on properties of the characteristic function of the stable distribution. This method has also been extensively discussed by Kogon and Williams (1998), so we give only a very brief discussion here.…”

Section: The Koutrouvelis Methodsmentioning

confidence: 99%

“…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%

“…Koutrouvelis (1980) indicates how to select appropriate λ-values. Thus by this method both α and c can be estimated.…”

Section: The Koutrouvelis Methodsmentioning

confidence: 99%

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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: Results For Norwaymentioning

confidence: 96%

Section: The Koutrouvelis Methodsmentioning

confidence: 99%

Section: The Koutrouvelis Methodsmentioning

confidence: 99%

“…Koutrouvelis (1980) indicates how to select appropriate λ-values. Thus by this method both α and c can be estimated.…”

Section: The Koutrouvelis Methodsmentioning

confidence: 99%

See 2 more Smart Citations

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

Dagsvik

Jia

Vatne³

et al. 2011

Empir Econ

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“…β = 0 indicates a distribution symmetric about δ. There are two algorithms provide consistent estimators for all four parameters-Koutrouvelis's method, which is based on empirical characteristic function methods of Koutrouvelis [24] and McCulloch's method, which is a simpler, faster but less accurate method [25]. In this paper, we apply Koutrouvelis method for estimation of these parameters in Section 4.…”

Section: α Stable Distributionmentioning

confidence: 99%

A Novel Method for Control Performance Assessment with Fractional Order Signal Processing and Its Application to Semiconductor Manufacturing

et al. 2018

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Abstract:The significant task for control performance assessment (CPA) is to review and evaluate the performance of the control system. The control system in the semiconductor industry exhibits a complex dynamic behavior, which is hard to analyze. This paper investigates the interesting crossover properties of Hurst exponent estimations and proposes a novel method for feature extraction of the nonlinear multi-input multi-output (MIMO) systems. At first, coupled data from real industry are analyzed by multifractal detrended fluctuation analysis (MFDFA) and the resultant multifractal spectrum is obtained. Secondly, the crossover points with spline fit in the scale-law curve are located and then employed to segment the entire scale-law curve into several different scaling regions, in which a single Hurst exponent can be estimated. Thirdly, to further ascertain the origin of the multifractality of control signals, the generalized Hurst exponents of the original series are compared with shuffled data. At last, non-Gaussian statistical properties, multifractal properties and Hurst exponents of the process control variables are derived and compared with different sets of tuning parameters. The results have shown that CPA of the MIMO system can be better employed with the help of fractional order signal processing (FOSP).

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