Critical Dstatistic table generation
Description
The Dstatistic
denotes the maximum
deviation of sequence from a hypothetical linear cumulative energy
trend. The critical Dstatistics
define the distribution of D for a
zero mean Gaussian white noise process. Comparing the sequence
Dstatistic
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.
Usage
1 2 3 
Arguments
lookup 
a logical flag for accessing precalculated
critical 
n.realization 
an integer specifying the number of realizations to generate in a
Monte Carlo simulation for calculating the 
n.repetition 
an integer specifying the number of Monte Carlo simulations to
perform. This parameter coordinates with the n.realization
parameter. Default: 
n.sample 
a vector of integers denoting the sample sizes for which critical

significance 
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.
Default: 
tolerance 
a numeric real scalar that specifies the amplitude threshold to use in
estimating critical 
Details
A precalculated critical Dstatistics
object
(D.table.critical
) exists
on the package workspace and was built for a variety of sample sizes and
significances using 3 repetitions and 10000
realizations/repetition. This D.table
function should be used in
cases where specific Dstatistic
s are missing from
D.table.critical
.
Note: the results of the D.table
value should not be returned to a
variable named D.table.critical
as it will override the
precalculated table available in the package.
An InclanTiao approximation of critical Dstatistics
is used for sample
sizes n.sample
>= 128 while a Monte Carlo technique is used for
n.sample
< 128. For the
Monte Carlo technique, the Dstatistic
for a
Gaussian white noise sequence of length n.sample
is calculated. This
process is repeated n.realization times, forming a distribution of the
Dstatistic
. The critical values corresponding to the significances
are calculated a total of n.repetition times, and averaged to form
an approximation to the Dstatistic(s)
.
Value
a matrix containing the critical
Dstatistics
corresponding to the supplied sample sizes and
significances.
References
D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000.
See Also
D.table.critical
.
Examples
1 2 