Binomial Distribution Handbook for Scientists and Engineers
This book deals with estimating and testing the probability of an event. The purpose of the book is twofold: It aims at providing practitioners with refined and easy to use techniques as well as initiating a new field of research in theoretical statistics
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Elart von Collani Klaus Drăger
Binomial Distribution Handbook for Scientists and Engineers
Springer Science+Business Media, LLC
Elart von Collani Klaus Drăger University of Wiirzburg Sanderring 2 D-97070 Wiirzburg Germany
Library of Congress Cataloging-in-Publication Data von Collani, Elart, 1944Binomial distribution handbook for scientists and engineers I Elart von Collani, Klaus p. cm. Includes bibliographical references and index. ISBN 978-1-4612-6666-2 ISBN 978-1-4612-0215-8 (eBook) DOI 10.1007/978-1-4612-0215-8 1. Binomial distribution. 1. Drăger, Klaus. QA273.6 .V65 2001
Drăger.
00-046821
5 12.2'4-dc2 1
CIP
Printed on acid-free paper. © 2001 Springer Science+Business Media New York Originally published by Birkhăuser Boston in 2001 Softcover reprint of the hardcover 1st edition 200 1
AlI rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC), except for brief excerpts in connection with reviews or scho1arly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimi1ar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even ifthe former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may according1y be used freely by anyone. Additional material to this book can be downloaded from http://extras.springer.com
ISBN 978-1-4612-6666-2
SPIN 10723723
Production managed by Louise Farkas; manufacturing supervised by Erica Bresler. Typeset by the author in LaTeX.
9 8 765 4 3 2 1
To Claudia and Machiko
Contents xiii
Preface
I
Introduction
1
1 Stochastics 1.1 The Science of Stochastics 1.2 Historical Remarks . . . . 1.3 Measurement Procedure and Measurement Range . . . . .
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2 Models Related to the Probability of an Event 2.1 The Concept of Probability 2.2 Random Variables and Data 2.3 The Model. . . . . . . . . 2.4 The Random Sample . . . . 2.5 The Binomial Distribution . 2.6 The Hypergeometric Distribution 2.7 Measuring in the Measurement Range.
12 12 16 17 19 21 27 28
3 Traditional Estimation Procedures 3.1 Theory of Estimation . . . . . . . . 3.1.1 Neyman's Approach . . . . 3.1.2 Point and Interval Estimation 3.2 Interval Estimator for a Probability . 3.3 The Relative Frequency X . . . . . . 3.4 Measurement Procedures Based on the Relative Frequency . . . . . . . . . . . . . . . . . . .
32 32 32 39 42 46
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CONTENTS
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3.4.1 3.4.2
II
Traditional Measurement Procedures Approximate Interval Estimators ..
Theory
4 Measurement and Prediction Procedures 4.1 The Problem Revisited . 4.2 Measurement & Prediction Space 4.2.1 Measurement & Prediction Space for (p, X) 4.2.2 Measurement & Prediction Space for (p, X s ) 4.3 ,B-Measurement & Prediction. . . 4.3.1 The ,B-Measurement & Prediction Space f
