{"title":"Some properties of the Blumberg's hyper-log-logistic curve","authors":"R. Anguelov, N. Kyurkchiev, S. Markov","doi":"10.11145/J.BIOMATH.2018.07.317","DOIUrl":null,"url":null,"abstract":"The paper considers the sigmoid function definedthrough the hyper-log-logistic model introduced by Blumberg. We study the Hausdorff distance of this sigmoid to the Heaviside function, which characterises the shape of switching from 0 to 1. Estimates of the Hausdorff distance in terms of the intrinsic growth rate are derived. We construct a family of recurrence generated sigmoidal functions based on the hyper-log-logistic function. Numerical illustrations are provided.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"27","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Biomath","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11145/J.BIOMATH.2018.07.317","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Agricultural and Biological Sciences","Score":null,"Total":0}
引用次数: 27
Abstract
The paper considers the sigmoid function definedthrough the hyper-log-logistic model introduced by Blumberg. We study the Hausdorff distance of this sigmoid to the Heaviside function, which characterises the shape of switching from 0 to 1. Estimates of the Hausdorff distance in terms of the intrinsic growth rate are derived. We construct a family of recurrence generated sigmoidal functions based on the hyper-log-logistic function. Numerical illustrations are provided.
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