Type: Package
Title: Detect and Test Regular Sequences and Subsequences
Version: 0.12
Date: 2014-03-06
Author: Yanming Di
Maintainer: Yanming Di<diy@stat.oregonstate.edu>
Description: For a sequence of event occurence times, we are interested in finding subsequences in it that are too "regular". We define regular as being significantly different from a homogeneous Poisson process. The departure from the Poisson process is measured using a L1 distance. See Di and Perlman 2007 for more details.
License: GPL-2
Packaged: 2014-03-09 17:49:22 UTC; yanming
Depends: R (≥ 2.10)
NeedsCompilation: no
Repository: CRAN
Date/Publication: 2014-03-09 19:18:52

Find the Most Gap-Linear Subsequence.

Description

Find the most gap-linear length k+1 subsequence of the input sequence. The subsequence found by this function has the same end points as the original sequence. This function is not intended to be used by an end user directly. Users should use test.gaplin.t, test.gaplin.p or test.gaplin instead.

Usage

  most.gaplin.sub(x, k, T);

Arguments

x

The input sequence, a vector of numbers.

k

The length of the subsequences for which we want to test gap-linearity.

T

A threshold value. A subsequence will only be examined when its gap-linearity test statistic can be bigger than this t.

Value

improved

TRUE if we found a subsequence with a gap-linearity test statistic more extreme than the input t.

t

The gap-linearity test statistic corresponding to the most gap-linear subsequence.

sub

The most gap-linear subsequence.

sigma

The indices corresponding to the most gap-linear subsequence.

Author(s)

Yanming Di

References

Di and Perlman (2007)

See Also

test.gaplin, test.gaplin.t, test.gaplin.p.

Find the Most Lineaer Subsequence

Description

Find the most linear length k+1 subsequence of the input sequence. The subsequence found by this function has the same end points as the original sequence. This function is not intended to be used by an end user directly. Users should use test.lin.t, test.lin.p or test.lin instead.

Usage

  most.linear.sub(x, k, t);

Arguments

x

The input sequence, a vector of numbers.

k

The length of the subsequences for which we want to test linearity.

t

A threshold value. A subsequence will only be examined when its linearity test statistic can be bigger than this t.

Value

improved

TRUE if we found a subsequence with a linearity test statistic more extreme than the input t.

t

The linearity test statistic corresponding to the most linear subsequence.

sub

The most linear subsequence.

sigma

The indices corresponding to the most linear subsequence.

Author(s)

Yanming Di

References

Di and Perlman (2007)

See Also

test.lin, test.lin.t, test.lin.p.

Quantile Tables of the Linearity/Gap-Linearity Tests

Description

The data set provide quantile tables for the linearity/gap-linearity test statistics for N=2, ..., 50 and k= 2, ..., N, for each N. These tables will be used to compute p-values corresponding to test statistics.

Usage

qtables

Format

R rda files. Within each quantile table, the first row indicates at which probability values the quantiles are computed.

Compute the Gap-Linearity Test Statistics

Description

An internal function used to recursively compte gap-linearity test statistics. This function is not intended to be used by an end user.

Usage

recursive.B(x, indices = FALSE);

Arguments

x

A sequence of numbers.

indices

Whether to keep track of indices of the end points of the most gap-linear subsequences.

Value

A table of computed test statistics. If indices is TRUE, almost return the indices of the end points of the most gap-linear subsequences.

Author(s)

Yanming Di

References

Di and Perlman (2007)

Detect and Test Almost Gap-Linear Subsequnces.

Description

test.gaplin.t find the most almost gap-linear length k+1 subsequence of a given sequence and compute the almost gap-linearity test statistic for this subsequence. test.gaplin.p compute the p-value corresponding to a computed test statistic. test.gaplin compute the test statistics and the p-values for subsequences of all lengths.

Usage

test.gaplin(Tn);
test.gaplin.t(Tn, k);
test.gaplin.p(t, n, k);

Arguments

Tn

A sequence of numbers. Currently, only support sequence of length less than 50.

k

The length of the subsequences for which we want to test for almost gap-linearity.

n

The length of the sequence for which we want to test for subsequence almost gap-linearity.

t

Test statistic computed for a length k+1 subsequence of a length n+1 sequence.

Details

Almost gap-linear means the spacings of a subsequence are almost in proportion to the spacings of the corresponding indicies. For example, for Tn=c(11, 14, (.), 20), the subs sequence (11, 14, 20) is gap-linear, since the spacings (3, 6) is in proportion with the spacings of hte corresponding indicies (1, 2). Equivalently, almost gap-linearity can measured by the distance between the standardized spacings of the subsequnce and the standardized spacings of the corresponding indicies. See Di and Perlman (2007) for more details.

Value

test.gaplin.t returns the most gap-linear length k+1 subsequence of the input sequence and corresponding almost gap-linearity test statistic. test.gaplin.p returns the p-value corresponding to the input test statistic t. test.lin has no return value, instead, a table containing the most almost gap-linear subsequences, corresponding test staistics and p-values will be outputed.

Author(s)

Yanming Di

References

Di and Perlman, 2007

See Also

test.lin.

Examples

  ## A sequence representing arrival times of events.
  Tn = c(13, 21, 24, 33, 40, 55, 59, 63, 72, 85, 87);

  ## Test for almost linearity.
  t = test.gaplin.t(Tn, 4);
  print(t$sub);
  p = test.gaplin.p(t$t, 10, 4);
  print(p);
  test.gaplin(Tn);

Detect and Test Almost Linear Subsequences.

Description

test.lin.t find the most almost-linear length k+1 subsequence of a given sequence and compute the almost-linearity test statistic for this subsequence. test.lin.p compute the p-value corresponding to a computed test statistic. test.lin compute the test statistics and the p-values for subsequences of all lengths.

Usage

test.lin(Tn);
test.lin.t(Tn, k);
test.lin.p(t, n, k);

Arguments

Tn

A sequence of numbers. Currently, only support sequences of length less than 50.

k

The length of the subsequences for which we want to test for almost-linearity.

n

The length of the sequence for which we want to test for subsequence almost-linearity.

t

Test statistic computed for a length k+1 subsequence of a length n+1 sequence.

Details

Almost-linear means the spacings of the sequence are almost equal, or the distance between the standardized spacings as a vector and (1/k, ..., 1/k) is too small. The p-value is computed by comparing the test statistic to a procomputed test statistic quantile table. See Di and Perlman (2007) for more details.

Value

test.lin.t returns the most linear length k+1 subsequence of the input sequence and corresponding almost-linearity test statistic. test.lin.p returns the p-value corresponding to the input test statistic t. test.lin has no return value, instead, a table containing the most almost linear subsequences, corresponding test staistics and p-values will be outputed.

Author(s)

Yanming Di

References

Di and Perlman, 2007

See Also

test.gaplin.

Examples

  ## A sequence representing arrival times of events.
  Tn = c(13, 21, 24, 33, 40, 55, 59, 63, 72, 85, 87);

  ## Test for almost linearity.
  t = test.lin.t(Tn, 4);
  print(t$sub);
  p = test.lin.p(t$t, 10, 4);
  print(p);
  test.lin(Tn);