Some Improvements in Numerical Evaluation of Symmetric Stable Density and Its Derivatives

DOI10.1080/03610920500439729zbMath1089.60015arXivmath/0408321OpenAlexW2158431768MaRDI QIDQ5201480

Muneya Matsui, Akimichi Takemura

Publication date: 19 April 2006

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0408321

zbMATH Keywords

maximum likelihood estimatorFisher information matrixstable distribution

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (16)

Estimating GARCH-type models with symmetric stable innovations: indirect inference versus maximum likelihood ⋮ Fractional absolute moments of heavy tailed distributions ⋮ Efficient estimation of stable Lévy process with symmetric jumps ⋮ Modeling and simulation studies for some truncated discrete distributions generated by stable densities ⋮ Asymptotics of maximum likelihood estimation for stable law with continuous parameterization ⋮ Bayesian inversion with α-stable priors ⋮ Joint estimation for SDE driven by locally stable Lévy processes ⋮ Maximum likelihood estimation for \(\alpha\)-stable double autoregressive models ⋮ Non-Gaussian quasi-likelihood estimation of SDE driven by locally stable Lévy process ⋮ Estimating stable latent factor models by indirect inference ⋮ Integral representations of one-dimensional projections for multivariate stable densities ⋮ Remarks on the stable \(S_{\alpha}(\beta, \gamma, \mu)\) distribution ⋮ Accurate and efficient numerical calculation of stable densities via optimized quadrature and asymptotics ⋮ On the confidence intervals of parametric functions for Distributions Generated by Symmetric Stable Laws ⋮ Goodness-of-fit tests for symmetric stable distributions-empirical characteristic function approach ⋮ Analytical-numeric formulas for the probability density function of multivariate stable and geo-stable distributions

Uses Software

• STABLE
• GSL

Cites Work

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• Parameterizations and modes of stable distributions
• On the asymptotic normality of the maximum-likelihood estimate when sampling from a stable distribution
• On some expansions of stable distribution functions
• Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests Under Nonstandard Conditions
• Some Properties of Symmetric Stable Distributions Close to the Normal Distribution
• Maximum Likelihood Estimates of Symmetric Stable Distribution Parameters
• Stable Distributions in Statistical Inference: 2. Information from Stably Distributed Samples
• Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information
• Numerical calculation of stable densities and distribution functions

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