Biometrical Journal / Biometrische Zeitschrift: Volume 27, Number 2 March 1985 [Reprint 2021 ed.] 9783112487822, 9783112487815

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BIDUETRICAL — MHil Journal of

Volume 27 • 1985 • Number 2

1 I

March

Akademie-Verlag • Berlin and VCH Publishers, Inc. • DeerfieldBeach/Florida ISSN 0323-3847

Biom. J . , Berlin 27 (1985) 2, 1 2 1 - 2 4 0

Information on the J o u r n a l Biometrical J o u r n a l was founded for t h e purpose of publishing contributions on mathematical penetration of biosciences. The scope includes papers on new theoretical aspects of mathematics and its application t o biological sciences in t h e widest sense (including biology, medicine, agricultural science, forestry) or on t h e application of known mathematical and statistical methods to new areas. These m a y be methods of mathematical statistics and approaches t o mathematico-cybernetik model construction of biological systems with due consideration of electronic d a t a processing. Accepted for publication: original papers, s u m m a r y reports on t h e latest developments in t h e above areas, proceedings and book reviews. Mailing address: Institut für Mathematik der AdW DDK - 1 0 8 6 Berlin Moürenstraße 39

Instructions for a u t h o r s : 1. Manuscripts should be submitted in two copies typed with double line spacing on one side of the page and with sufficient margin. Authors are expected to keep one complete copy of their paper for themselves. A manuscript should not be longer t h a n 30 typewritten pages. 2. The institute a t which the work on t h e paper was done should be listed below the n a m e of t h e author (with t h e initials of his Christian names) below t h e title. 3. The full address of t h e author must be listed a t t h e end of the paper. 4. Each original paper should include an abstract a n d two summaries, one in the language of t h e paper and t h e other in one of t h e publication languages (German, English, French, Russian). 5. Illustrations and captions must be enclosed separately and t h e y should be continuously numbered. The number of illustrations should be k e p t as small as possible. 6. Special markings in colour (e.g. for formulae) should be avoided. 7. Smaller t y p e for a section of t h e t e x t should be denoted b y a vertical stroke d r a w n a t t h e left on t h e section concerned and by writing t h e instruction "smaller t y p e " in t h e margin space n e x t to the stroke. 8. Literature in the t e x t should be quoted together with t h e n a m e of the author and t h e year of publication. Each paper has t o be completed b y a list of references specifying t h e n a m e and initials of the Christian names of the author, year, title of paper, name of journal, volume, issue, and for books also t h e place of publication. 9. Corrections or changes of t h e paper must be avoided after t h e manuscript has been typeset. The publishers reserve t h e right to charge t h e a u t h o r for corrections t h a t exceed t e n per cent of the overall cost of typesetting. 10. Each author is entitled to receive 50 reprints free of charge and up to 100 additional copies on p a y m e n t .

BIOMETRISCHE ZEITSCHRIFT J o u r n a l of Mathematical Methods in Biosciences Zeitschrift f ü r mathematische Methoden in den Biowissenschaften

Edited at I n s t i t u t e of Mathematics Aeadenn of ¡Silences of the G.D.R. b\ Erna Weber (Berlin), Editor-in-Chief Editors Heinz Ahrens (Berlin), Klaus Belljnann (Berlin) Editorial Board J . Adam (Halle), G. Enderlein (Berlin), D . J . Finney (Edinburgh), D. Firescu (Bucharest). B. W. Gnedenko (Mosco«), ¡S. Koller (Mainz), H. L. Le Roy (Zurich), C. C. Li (Pittsburgh), G. A. Lienert (Nuremberg), A. Linder (Geneva),

Volume 27 1985 Number 2

L. Martin (Brussels), \Y. Oehmisch (Berlin), T. Postelnicu (Bucharest), D. Rasch (Rostock), V. A. R a t n e r (Novosibirsk), J . - H . Scharf (Halle), L. Schmetterer (Vienna), D. Stoyan (Freiberg), P. T a u t u (Heidelberg), R. T r o m m e r (Eberswalde)

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Biometrial Journal Herausgeber: Prof. Dr. habil. Dr. h. c. Erna Weber, Institut für Mathematik der AdW, DDR - 1086 Berlin, Mohrenstraße 39. Verlag: Akademie-Verlag, D D R - 1086 Berlin, Leipziger Straße 3 - 4 ; Fernruf: 2 23 62 01 oder 2 23 62 29; Telex-Nr.: 1144 20; Bank: Staatsbank der D D R , Berlin, Kto-Nr.: 6826-26-20712. Chefredaktion: Prof. Dr. habil. H. Ahrens und Dr. habil. K. Bellmann. Anschrift der Redaktion: Institut für Mathematik der AdW, DDR - 1086 Berlin, Mohrenstraße 39. Veröffentlicht unter der Lizenznummer 1335 des Presseamtes beim Vorsitzenden des Ministerrates der Deutschen Demokratischen Republik. Gesamtherstellung: VEB Druckerei »Gottfried Wilhelm Leibniz«, D D R - 4450 Gräfenhainichen. Erscheinungsweise: Die Zeitschrift erscheint jährlich in einem Band mit 8 Heften. Bestellnummer dieses Heftes: 1060/27/2. Urheberrecht: Alle Rechte vorbehalten insbesondere die der Übersetzung. Kein Teil dieser Zeitschrift darf in irgendeiner Form — durch Photokopie, Mikrofilm oder irgendein anderes Verfahren — ohne schriftliche Genehmigung des Verlages reproduziert oder in eine von Maschinen, insbesondere von Datenverarbeitungsanlagen verwendbare Sprache übertragen oder übersetzt werden. All rights reserved (including those of translation into foreign languages). No part of this issue m a y be reproduced in any form by photoprint, microfilm or any other means, nor transmitted or translated into a machine language, without written permission from the publishers. © 1985 by Akademie-Verlag Berlin. Printed in the German Democratic Republic.

B i o m . J . 27 (1985) 2, 1 2 3 - 1 3 8

Robust Univariate Two-Way Classification1 N. B a l a k r i s h n a n

and

M. L.

Tiku

Department of Mathematical Sciences McMaster University, Hamilton, Ontario, Canada

A. H . El.

S h a a r a w i

National Water Research Institute, Ontario

Abstract We develop a robust classification procedure, based on T i k t j ' s (1967, 1980, 1982) MML (modified maximum likelihood) estimators, for classifying an observation in one of the two populations and 7t/2> (FT! - ix2)io2

.

The distribution of U is clearly normal with mean E(U

and

\x0£7ii)=d/2

E(i7 | X0£tc2) = -6/2

and variance (2.5)

Var (U) = 6;

)2/o2 is the standardized distance between the two populations and 7i)Under the assumption of normality, the asymptotic value of C is given by (2.6)

(e1 = 0.05) .

C = (d/2)-lMfd,

However, C cannot be determined since