Invariance conditions for random curvature models
type: Item
instance of: scholarly article
title: Invariance conditions for random curvature models
zbMATH Open document ID: 1054.92024
DOI: 10.1023/A:1026285429743
author: Marlos A. G. Viana
published in: Methodology and Computing in Applied Probability
publication date: 2004-01-05T00:00:00Z
review text: The author introduces a class of probability laws suggesed by the geometric optics of the human eye. These models are concerned with the representation of random corneal curvature measurements \(y\) indexed by concentric equally-spaced locations \(v= \{\theta_1,\theta_2,\dots, \theta_\ell\}\). He considers the effect that the symmetries imposed on the probability law of \(y\) have on the probability law for the ranking permutations associated with the ordering of the observed curvatures, as well as on the resolution geometric optics (astigmatic or sitmatic) that is consistent with these symmetries. In Section 2, after the definitions of astigmatic and stigmatic probability laws, the notations and structured data formulations needed for the remaining sections are given. In Section 3, the first moments of the angular variation are derived when the law of \(y\) is permutation symmetric. The case of finite-valued curvatures is discussed in Section 4, whereas a constructive rule for obtaining astigmatic laws is introduced in Section 5. Additional comments and technical definitions are given in Section 6.
Mathematics Subject Classification ID: 92C30
Mathematics Subject Classification ID: 15B52
Mathematics Subject Classification ID: 20B30
Mathematics Subject Classification ID: 78A70
zbMATH DE Number: 2021292
zbMATH Keywords: corneal curvature
zbMATH Keywords: random matrices
zbMATH Keywords: symmetric groups
zbMATH Keywords: structured data
zbMATH Keywords: orbits
zbMATH Keywords: keratometry
reviewed by: Takayuki Nôno
MaRDI profile type: Publication
full work available at URL: a:1026285429743
OpenAlex ID: W2170302170
description: scientific article; zbMATH DE number 2021292