Critical D-statistic table generation
D-statistic denotes the maximum
deviation of sequence from a hypothetical linear cumulative energy
trend. The critical
D-statistics define the distribution of D for a
zero mean Gaussian white noise process. Comparing the sequence
D-statistic to the corresponding critical
values provides a means of quantitatively rejecting or accepting the
linear cumulative energy hypothesis. The table is generated for an
ensemble of distribution probabilities and sample sizes.
1 2 3
a logical flag for accessing precalculated
an integer specifying the number of realizations to generate in a
Monte Carlo simulation for calculating the
an integer specifying the number of Monte Carlo simulations to
perform. This parameter coordinates with the n.realization
a vector of integers denoting the sample sizes for which critical
a numeric vector of real values in the interval (0,1).
The significance is the fraction of times that the
linear cumulative energy hypothesis is incorrectly rejected. It is
equal to the difference of the distribution probability (p) and unity.
a numeric real scalar that specifies the amplitude threshold to use in
A precalculated critical
on the package workspace and was built for a variety of sample sizes and
significances using 3 repetitions and
D.table function should be used in
cases where specific
D-statistics are missing from
Note: the results of the
D.table value should not be returned to a
D.table.critical as it will override the
precalculated table available in the package.
An Inclan-Tiao approximation of critical
D-statistics is used for sample
n.sample >= 128 while a Monte Carlo technique is used for
n.sample < 128. For the
Monte Carlo technique, the
D-statistic for a
Gaussian white noise sequence of length
n.sample is calculated. This
process is repeated n.realization times, forming a distribution of the
D-statistic. The critical values corresponding to the significances
are calculated a total of n.repetition times, and averaged to form
an approximation to the
a matrix containing the critical
D-statistics corresponding to the supplied sample sizes and
D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000.
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