A generalization of Student'st-distribution from the viewpoint of special functions

DOI10.1080/10652460600856419zbMath1109.60010OpenAlexW2033914167MaRDI QIDQ3423553

Mohammad Masjed-Jamei, Wolfram Koepf

Publication date: 14 February 2007

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460600856419

zbMATH Keywords

normal distributionchi-square distributiongamma distributionStudent \(t\)-distributionCauchy integral: Fisher \(F\)-distribution

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Probability distributions: general theory (60E05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items (6)

A new asymptotic representation and inversion method for the Student's t distribution ⋮ Incomplete symmetric orthogonal polynomials of finite type generated by a generalized Sturm–Liouville theorem ⋮ Explicit barycentric formulae for osculatory interpolation at roots of classical orthogonal polynomials ⋮ Sixth-kind Chebyshev spectral approach for solving fractional differential equations ⋮ Polynomial extensions of distributions and their applications in actuarial and financial modeling ⋮ The Szegö-Markov-Bernstein inequalities and barycentric representations of the osculatory interpolating operators for classical iterated weights

Cites Work

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• Three Finite Classes of Hypergeometric Orthogonal Polynomials and Their Application in Functions Approximation
• Classical orthogonal polynomials with weight function ((ax + b)² + (cx + d)²)^−pexp(qArctg((ax + b)/(cx + d))),x ∈ (−∞, ∞) and a generalization of T and F distributions

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