The study of a function relating to stable distributions
type: Item
instance of: scholarly article
title: The study of a function relating to stable distributions
zbMATH Open document ID: 0819.60018
DOI: 10.1016/0167-7152(94)90022-1
author: D. J. Buckle
published in: Statistics \& Probability Letters
publication date: 1995-08-21T00:00:00Z
review text: The real function \[ t_{\alpha, \beta} (\theta) = \left( {\sin (\pi \alpha \theta + \eta_{\alpha, \beta}) \over \cos \pi \theta} \right) \left( {\cos \pi \theta \over \cos \bigl[ \pi (\alpha - 1) \theta + \eta_{\alpha, \beta} \bigr]} \right)^{(\alpha - 1)/ \alpha}, \quad - 1/2 < \theta < 1/2, \] appears in the representation of distribution functions for stable laws, see \textit{V. M. Zolotarev} [Select. Transl. Math. Stat. Probab. 6, 84-88 (1966); translation from Trudy Mat. Inst. Steklova. 71, 46-50 (1964; Zbl 0154.194)]. The values \(\eta_{\alpha, \beta}\) are certain constants. The author studies this function in detail: symmetry, zeros, continuity, monotonicity, first derivative.
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 33B99
zbMATH DE Number: 633684
zbMATH Keywords: stable distribution
zbMATH Keywords: trigonometric identity
reviewed by: Arnold Janssen
MaRDI profile type: Publication
full work available at URL: 0167-7152(94)90022-1
OpenAlex ID: W2030171648
cites work: Bayesian Inference for Stable Distributions
cites work: A Method for Simulating Stable Random Variables
cites work: Q4739659
cites work: Q5601177
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description: scientific article; zbMATH DE number 633684