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

By Muneya Matsui, Akimichi Takemura. 2004

52 citations recorded by the source corpus.

ABSTRACT We propose improvements in numerical evaluation of symmetric stable density and its partial derivatives with respect to the parameters. They are useful for more reliable evaluation of maximum likelihood estimator and its standard error. Numerical values of the Fisher information matrix of symmetric stable distributions are also given. Our improvements consist of modification of the method of Nolan (1997) for the boundary cases, i.e., in the tail and mode of the densities and in the neighborhood of the Cauchy and the normal distributions.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/380ba77520d0f201bc8c6160f43966baebefa689

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Rafal Weron
2. Akimichi Takemura
3. Muneya Matsui
4. Adam Misiorek
5. Szymon Borak
6. John P. Nolan
7. Florian Ziel
8. Jakub Nowotarski

In Finance

1. Muneya Matsui
2. Akimichi Takemura
3. Rafal Weron
4. Adam Misiorek
5. Szymon Borak
6. John P. Nolan
7. Ladislav Kristoufek
8. Simos G. Meintanis

In Statistics and Probability

1. John P. Nolan
2. Muneya Matsui
3. Akimichi Takemura
4. Rafal Weron
5. Szymon Borak
6. Adam Misiorek
7. Jan W. H. Swanepoel
8. Simos G. Meintanis

Citations in the corpus

• Goodness-of-fit tests for symmetric stable distributions—Empirical characteristic function approach (2006, methodology): “We utilize asymptotic expansions of f(x;α) and fθ(x;α) in Matsui and Takemura (2006): f(x;α) = 1 π ∞ ∑ k=1 Γ(kα+ 1) k!”
• Models for Heavy-tailed Asset Returns (2010, methodology): “Matsui and Takemura (2006) further improved Nolan’s method for the boundary cases, i.e. in the tail and mode of the densities and in the neighborhood of the Cauchy and the Gaussian distributions, but only in the symmetric stable case. As Ojeda (2001) observes, the ML estimates are almost always the ”
• Bibliography on stable distributions, processes and related topics (2004, background): “…Yanushkevichiene and Saenko (2013), Saenko (2016), Barker (2014), Basu and Pakrashi (2018), Meraghni and Soltane (2019), Fahs and Abou-Faycal (2018) Calculation of Fisher information matrix for MLE of stable parameters: DuMouchel (1973a), Nolan (2001a), Matsui and Takemura (2004), Barker (2015).”