On the errors of misclassification based on dichotomous and normal variables
type: Item
instance of: scholarly article
title: On the errors of misclassification based on dichotomous and normal variables
zbMATH Open document ID: 0631.62074
author: Subrahmaniam Kocherlakota
author: K. Kocherlakota
author: Narayanaswamy Balakrishnan
published in: Annals of the Institute of Statistical Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Für den Vektor \(W'=(X,Y)\) einer Normalverteilung und einer binomial verteilten Zufallsgröße werden Beobachtungen in zwei Populationen \(\Pi_ 1\) und \(\Pi_ 2\) klassiert, wobei \(\Pi_ i\) die Wahrscheinlichkeitsdichte \[ f_ i(w)=\theta^ x_ i(1-\theta_ i)^{1-x}\Phi (y;\quad \mu_ i^{(x)},\quad \sigma^{(x)^ 2}),\quad i=1,2, \] hat. Under der Voraussetzung der Varianzgleichheit von Y unter \(\Pi_ 1\) und \(\Pi_ 2\), aber bei \(Var(W| \Pi_ 1)\neq Var(W| \Pi_ 2)\), werden die Klassifikationsfehler \(e_{12}=P(Fehlklassifikation\) von w in \(\Pi_ 2\), wenn w aus \(\Pi_ 1\) stammt) \(und\) e\({}_{21}=P(Fehlklassifikation\) von w in \(\Pi_ 1\), wenn w aus \(\Pi_ 2\) stammt) für die Fälle betrachtet, daß alle Parameter bekannt bzw. unbekannt sind. Die Erwartungswerte \(E(e_{12})\) und \(E(e_{21})\) werden bestimmt.
Mathematics Subject Classification ID: 62H30
zbMATH DE Number: 4026600
zbMATH Keywords: errors of misclassification
zbMATH Keywords: dichotomous variables
zbMATH Keywords: normal distribution
zbMATH Keywords: distribution of errors of misclassification
MaRDI profile type: Publication
cites work: Classification Based on Dichotomous and Continuous Variables
cites work: Robustness of the linear discriminant function to nonnormality: Johnson's system
cites work: Q4179693
cites work: Errors in Discrimination
cites work: Robustness of the linear discriminant function to nonnormality: Edgeworth series distribution
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description: scientific article; zbMATH DE number 4026600