The Statistical Analysis of Series of EventsObservations in the form of point events occurring in a continuum, space or time, arise in many fields of study. In writing this monograph on statistical techniques for dealing with such data, we have three objectives. First, we have tried to give a simple description, with numerical examples, of the main methods that have been proposed. We hope that by concentrating on the examples the applied statistician with a limited inclination for theory will find something of practical value in the monograph. Second, the monograph is intended as a survey, necessarily incomplete, of some of the problems in theoretical statistics that stem from this sort of data. A number of specialized subjects have, however, been dealt with only briefly, the main emphasis being placed on the problem of examining the structure of a series of events. Finally, we hope that the monograph will be of use to teachers and students of statistics, as illustrating applications of a range of tech niques in theoretical statistics. We are extremely grateful to the International Business Machines Corporation for providing programming assistance and a large amount of computer time. We wish to thank particularly Mr A. |
Contents
Estimation of SecondOrder Properties of Stationary Pro | 85 |
Renewal Processes and Some Related Significance Tests | 134 |
Generalizations of Renewal Processes | 179 |
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analysis approximation asymptotic Bartlett branching Poisson process cent Chapter chi-squared distribution coefficient of variation component processes computer data consider covariance density degrees of freedom denote discussed distribution of intervals distribution-free empirical distribution function equation error estimate events occur exponential distribution failure Fn(x Fo(x g+(w Gamma distribution give given goodness-of-fit independent intensity function intervals between successive intervals of length linear Markov maximum likelihood mean methods normal distribution null hypothesis number of events obtained parameter period of observation Poisson distribution Poisson hypothesis Poisson process pooled output probability problem random variables rate of occurrence second-order properties Section semi-Markov process sequence serial correlation serial correlation coefficients series of events spectral density spectrum of counts spectrum of intervals stationary process successive events survivor function Table test statistic tests based tests for Poisson tion transform trend type I event var(X variance variance-time curve weight function zero