Properties of powers of functions satisfying second-order linear differential equations with applications to statistics

DOI10.1007/s13160-015-0179-3zbMath1325.33016arXiv1405.4451OpenAlexW1568844618MaRDI QIDQ495859

Akimichi Takemura, Naoki Marumo, Toshinori Oaku

Publication date: 15 September 2015

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.4451

zbMATH Keywords

characteristic functionexponentsskewnessholonomic functionindicial equation

Mathematics Subject Classification ID

Exact distribution theory in statistics (62E15) Other functions coming from differential, difference and integral equations (33E30) Rings of differential operators (associative algebraic aspects) (16S32)

Uses Software

• DLMF
• hgm R

Cites Work

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• The holonomic gradient method for the distribution function of the largest root of a Wishart matrix
• The concrete tetrahedron. Symbolic sums, recurrence equations, generating functions, asymptotic estimates
• Holonomic gradient descent and its application to the Fisher-Bingham integral
• Algorithms for \(b\)-functions, restrictions, and algebraic local cohomology groups of \(D\)-modules
• Algorithms for integrals of holonomic functions over domains defined by polynomial inequalities
• Gröbner Bases
• Distributions and Operators
• Creative Telescoping for Holonomic Functions
• On the asymptotic expansion of Airy's Integral
• TESTING FOR NORMALITY

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