On the logistic midrange
type: Item
instance of: scholarly article
title: On the logistic midrange
zbMATH Open document ID: 0638.62014
DOI: 10.1007/BF02491495
published in: Annals of the Institute of Statistical Mathematics
publication date: 1987-01-01T00:00:00Z
review text: It is well-known that for a large family of distributions, the sample midrange is asymptotically logistic. In this article, the logistic midrange is closely examined. Its distribution function is derived using Dixon's formula [see \textit{W. N. Bailey}, Generalized hypergeometric series. (1935; Zbl 0011.02303)] for the generalized hypergeometric function with unit argument, together with appropriate techniques for the inversion of (bilateral) Laplace transforms. Several relationships in distribution are established between the midrange and sample median of the logistic and Laplace random variables. Possible applications in testing for outliers are also discussed.
Mathematics Subject Classification ID: 62E15
Mathematics Subject Classification ID: 33C60
Mathematics Subject Classification ID: 62E10
zbMATH DE Number: 4041032
zbMATH Keywords: inversion of bilateral Laplace transforms
zbMATH Keywords: characteristic functions
zbMATH Keywords: logistic distribution
zbMATH Keywords: Laplace distribution
zbMATH Keywords: sample midrange
zbMATH Keywords: logistic midrange
zbMATH Keywords: Dixon's formula
zbMATH Keywords: sample median
zbMATH Keywords: testing for outliers
author: E. Olusegun George
author: Cecil Rousseau
MaRDI profile type: Publication
cites work: The \(n^{-2}\)-order mean squared errors of the maximum likelihood and the minimum logit chi-square estimator
cites work: Q4760447
cites work: Q5598050
cites work: Q4162318
cites work: Ranges and Midranges
cites work: Q5624248
cites work: Q5585020
full work available at URL: https://doi.org/10.1007/bf02491495
OpenAlex ID: W2078563609
description: scientific article; zbMATH DE number 4041032