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NOTES ON STATISTICS FOR PHYSICISTS, REVISED

Jay Orear


Laboratory for Nuclear Studies
Cornell University
Ithaca, NY 14853


Table of Contents

ORIGINAL PREFACE

PREFACE TO REVISED EDITION

DIRECT PROBABILITY

INVERSE PROBABILITY

LIKELIHOOD RATIOS

MAXIMUM-LIKELIHOOD METHOD

GAUSSIAN DISTRIBUTIONS

MAXIMUM-LIKELIHOOD ERROR, ONE PARAMETER

MAXIMUM-LIKELIHOOD ERRORS, M-PARAMETERS CORRELATED ERRORS

PROPAGATION OF ERRORS: THE ERROR MATRIX

SYSTEMATIC ERRORS

UNIQUENESS OF MAXIMUM-LIKELIHOOD SOLUTION

CONFIDENCE INTERVALS AND THEIR ARBITRARINESS

BINOMIAL DISTRIBUTION

POISSON DISTRIBUTION

GENERALIZED MAXIMUM-LIKELIHOOD METHOD

THE LEAST-SQUARES METHOD

GOODNESS OF FIT, THE chi2 DISTRIBUTION

APPENDIX I: PREDICTION OF LIKELIHOOD RATIOS

APPENDIX II: DISTRIBUTION OF THE LEAST-SQUARES SUM

APPENDIX III. LEAST SQUARES WITH ERRORS IN BOTH VARIABLES

APPENDIX IV. NUMERICAL METHODS FOR MAXIMUM LIKELIHOOD AND LEAST SQUARES SOLUTIONS

APPENDIX V. CUMULATIVE GAUSSIAN AND CGI-SQUARED DISTRIBUTIONS

REFERENCES



Erratum: The correct formula for the square root of the variance of a binomial distribution is sigma(p) = [p(1 - p) / N]1/2, where N is the number of trials and p is the probability of success.

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