Description Usage Format M. S. Bartlett's notes Source Examples
This is an example data set Bartlett used for a lecture course on
stochastic processes, Statistics Department, University College, London.
The data represents the times, in seconds, when cars passed an observation point
by a road.
Bartlett attributes the data to a Dr A. J. Miller who supplied them as a class example. According to Adery C. A. Hope the data was recorded on a rural Swedish road.
1 |
A numeric vector representing time points in seconds
Analyse the above data with a view to examining:
whether the times of passing constitute a Poisson process;
if not, whether some form of "bunching" or "clustering" seems to be present.
Possible analyses include:
testing the homogeneity of the consecutive random time-intervals, by means of a partitioning of the degrees of freedom for the total (approximate) χ^2;
testing the homogeneity of counts in consecutive fixed time-intervals, choosing an appropriate interval, and partitioning the degrees of freedom corresponding to the total dispersion by means of an analysis of variance;
testing the correlation between the consecutive random time-intervals;
examining the overall distribution of counts in fixed time-intervals;
examining the overall distribution of the consecutive random time-intervals
You should undertake at least sufficient of these to answer the questions asked.
The Spectral Analysis of Point Processes (p. 280), M. S. Bartlett, 1963
Also mentioned in:
Statistical Estimation of Density Functions (p. 252), M. S. Bartlett, 1963
A Simplified Monte Carlo Significance Test Procedure (p. 583),
Adery C. A. Hope, 1968
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | cpgram(diff(bartlett))
bartlett2 <- bartlett - bartlett[1]
x <- rep(0, tail(bartlett2, 1)*10)
x[bartlett2*10] <- 1
par(mfrow=c(2, 1), mar=c(2, 3, 1, 1))
plot(x, type="l", ann=FALSE)
lines(cumsum(x)/sum(x), col="red", lwd=2)
sp <- spectrum(x, main="", xlim=c(0, 0.1), ylim=c(1e-3, 0.04))
spec <- predict(loess(sp$spec[1:3000] ~ sp$freq[1:3000], span=0.15), se=TRUE)
lines(sp$freq[1:3000], spec$fit, col="red", lwd=2)
lines(sp$freq[1:3000], spec$fit - qt((0.99 + 1)/2, spec$df)*spec$se,
lty=1, col="lightblue")
lines(sp$freq[1:3000], spec$fit + qt((0.99 + 1)/2, spec$df)*spec$se,
lty=1, col="lightblue")
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