The regsubseq Package

Transcription

1 The regsubseq Package Sepember 30, 2007 Type Package Tile Deec and Tes Regular Sequences and Subsequences Version 0.10 Dae Auhor Mainainer For a sequence of even occurence imes, we are ineresed in finding subsequences in i ha are oo regular. We define regular as being significanly differen from a homogeneous Poisson process. The deparure from he Poisson process is measured using a L1 disance. See Di and Perlman 2007 for more deails. License GPL 2. R opics documened: mos.gaplin.sub mos.linear.sub qables recursive.b es.gaplin es.lin Index 8 1

2 2 mos.gaplin.sub mos.gaplin.sub Find he Mos Gap-Linear Subsequence. Find he mos gap-linear lengh k+1 subsequence of he inpu sequence. The subsequence found by his funcion has he same end poins as he original sequence. This funcion is no inended o be used by an end user direcly. Users should use es.gaplin., es.gaplin.p or es.gaplin insead. mos.gaplin.sub(x, k, T); x k T The inpu sequence, a vecor of numbers. The lengh of he subsequences for which we wan o es gap-lineariy. A hreshold value. A subsequence will only be examined when is gap-lineariy es saisic can be bigger han his. improved sub sigma TRUE if we found a subsequence wih a gap-lineariy es saisic more exreme han he inpu. The gap-lineariy es saisic corresponding o he mos gap-linear subsequence. The mos gap-linear subsequence. The indices corresponding o he mos gap-linear subsequence. Auhor(s) Di and Perlman (2007) See Also es.gaplin, es.gaplin., es.gaplin.p.

3 mos.linear.sub 3 mos.linear.sub Find he Mos Lineaer Subsequence Find he mos linear lengh k+1 subsequence of he inpu sequence. The subsequence found by his funcion has he same end poins as he original sequence. This funcion is no inended o be used by an end user direcly. Users should use es.lin., es.lin.p or es.lin insead. mos.linear.sub(x, k, ); x k The inpu sequence, a vecor of numbers. The lengh of he subsequences for which we wan o es lineariy. A hreshold value. A subsequence will only be examined when is lineariy es saisic can be bigger han his. improved sub sigma TRUE if we found a subsequence wih a lineariy es saisic more exreme han he inpu. The lineariy es saisic corresponding o he mos linear subsequence. The mos linear subsequence. The indices corresponding o he mos linear subsequence. Auhor(s) Di and Perlman (2007) See Also es.lin, es.lin., es.lin.p.

4 4 recursive.b qables Quanile Tables of he Lineariy/Gap-Lineariy Tess The daa se provide quanile ables for he lineariy/gap-lineariy es saisics for N=2,..., 50 and k= 2,..., N, for each N. These ables will be used o compue p-values corresponding o es saisics. qables Forma R rda files. Wihin each quanile able, he firs row indicaes a which probabiliy values he quaniles are compued. recursive.b Compue he Gap-Lineariy Tes Saisics An inernal funcion used o recursively compe gap-lineariy es saisics. This funcion is no inended o be used by an end user. recursive.b(x, indices = FALSE); x indices A sequence of numbers. Wheher o keep rack of indices of he end poins of he mos gap-linear subsequences. A able of compued es saisics. If indices is TRUE, almos reurn he indices of he end poins of he mos gap-linear subsequences. Auhor(s) Di and Perlman (2007)

5 es.gaplin 5 es.gaplin Deec and Tes Almos Gap-Linear Subsequnces. es.gaplin. find he mos almos gap-linear lengh k+1 subsequence of a given sequence and compue he almos gap-lineariy es saisic for his subsequence. es.gaplin.p compue he p-value corresponding o a compued es saisic. es.gaplin compue he es saisics and he p-values for subsequences of all lenghs. es.gaplin(tn); es.gaplin.(tn, k); es.gaplin.p(, n, k); Tn k n A sequence of numbers. Currenly, only suppor sequence of lengh less han 50. The lengh of he subsequences for which we wan o es for almos gap-lineariy. The lengh of he sequence for which we wan o es for subsequence almos gap-lineariy. Tes saisic compued for a lengh k+1 subsequence of a lengh n+1 sequence. Deails Almos gap-linear means he spacings of a subsequence are almos in proporion o he spacings of he corresponding indicies. For example, for Tn=c(11, 14, (.), 20), he subs sequence (11, 14, 20) is gap-linear, since he spacings (3, 6) is in proporion wih he spacings of he corresponding indicies (1, 2). Equivalenly, almos gap-lineariy can measured by he disance beween he sandardized spacings of he subsequnce and he sandardized spacings of he corresponding indicies. See Di and Perlman (2007) for more deails. es.gaplin. reurns he mos gap-linear lengh k+1 subsequence of he inpu sequence and corresponding almos gap-lineariy es saisic. es.gaplin.p reurns he p-value corresponding o he inpu es saisic. es.lin has no reurn value, insead, a able conaining he mos almos gap-linear subsequences, corresponding es saisics and p-values will be oupued. Auhor(s)

6 6 es.lin Di and Perlman, 2007 See Also es.lin. Examples ## A sequence represening arrival imes of evens. Tn = c(13, 21, 24, 33, 40, 55, 59, 63, 72, 85, 87); ## Tes for almos lineariy. = es.gaplin.(tn, 4); prin($sub); p = es.gaplin.p($, 10, 4); prin(p); es.gaplin(tn); es.lin Deec and Tes Almos Linear Subsequences. es.lin. find he mos almos-linear lengh k+1 subsequence of a given sequence and compue he almos-lineariy es saisic for his subsequence. es.lin.p compue he p-value corresponding o a compued es saisic. es.lin compue he es saisics and he p-values for subsequences of all lenghs. es.lin(tn); es.lin.(tn, k); es.lin.p(, n, k); Tn k n A sequence of numbers. Currenly, only suppor sequences of lengh less han 50. The lengh of he subsequences for which we wan o es for almos-lineariy. The lengh of he sequence for which we wan o es for subsequence almoslineariy. Tes saisic compued for a lengh k+1 subsequence of a lengh n+1 sequence.

7 es.lin 7 Deails Almos-linear means he spacings of he sequence are almos equal, or he disance beween he sandardized spacings as a vecor and (1/k,..., 1/k) is oo small. The p-value is compued by comparing he es saisic o a procompued es saisic quanile able. See Di and Perlman (2007) for more deails. es.lin. reurns he mos linear lengh k+1 subsequence of he inpu sequence and corresponding almos-lineariy es saisic. es.lin.p reurns he p-value corresponding o he inpu es saisic. es.lin has no reurn value, insead, a able conaining he mos almos linear subsequences, corresponding es saisics and p-values will be oupued. Auhor(s) See Also Di and Perlman, 2007 es.gaplin. Examples ## A sequence represening arrival imes of evens. Tn = c(13, 21, 24, 33, 40, 55, 59, 63, 72, 85, 87); ## Tes for almos lineariy. = es.lin.(tn, 4); prin($sub); p = es.lin.p($, 10, 4); prin(p); es.lin(tn);

8 Index Topic daases qables, 3 Topic hes es.gaplin, 4 es.lin, 6 Topic inernal mos.gaplin.sub, 1 mos.linear.sub, 2 recursive.b, 4 mos.gaplin.sub, 1 mos.linear.sub, 2 q.esgaplin.n10 (qables), 3 q.esgaplin.n11 (qables), 3 q.esgaplin.n12 (qables), 3 q.esgaplin.n13 (qables), 3 q.esgaplin.n14 (qables), 3 q.esgaplin.n15 (qables), 3 q.esgaplin.n16 (qables), 3 q.esgaplin.n17 (qables), 3 q.esgaplin.n18 (qables), 3 q.esgaplin.n19 (qables), 3 q.esgaplin.n2 (qables), 3 q.esgaplin.n20 (qables), 3 q.esgaplin.n21 (qables), 3 q.esgaplin.n22 (qables), 3 q.esgaplin.n23 (qables), 3 q.esgaplin.n24 (qables), 3 q.esgaplin.n25 (qables), 3 q.esgaplin.n26 (qables), 3 q.esgaplin.n27 (qables), 3 q.esgaplin.n28 (qables), 3 q.esgaplin.n29 (qables), 3 q.esgaplin.n3 (qables), 3 q.esgaplin.n30 (qables), 3 q.esgaplin.n31 (qables), 3 q.esgaplin.n32 (qables), 3 q.esgaplin.n33 (qables), 3 q.esgaplin.n34 (qables), 3 q.esgaplin.n35 (qables), 3 q.esgaplin.n36 (qables), 3 q.esgaplin.n37 (qables), 3 q.esgaplin.n38 (qables), 3 q.esgaplin.n39 (qables), 3 q.esgaplin.n4 (qables), 3 q.esgaplin.n40 (qables), 3 q.esgaplin.n41 (qables), 3 q.esgaplin.n42 (qables), 3 q.esgaplin.n43 (qables), 3 q.esgaplin.n44 (qables), 3 q.esgaplin.n45 (qables), 3 q.esgaplin.n46 (qables), 3 q.esgaplin.n47 (qables), 3 q.esgaplin.n48 (qables), 3 q.esgaplin.n49 (qables), 3 q.esgaplin.n5 (qables), 3 q.esgaplin.n50 (qables), 3 q.esgaplin.n6 (qables), 3 q.esgaplin.n7 (qables), 3 q.esgaplin.n8 (qables), 3 q.esgaplin.n9 (qables), 3 q.eslin.n10 (qables), 3 q.eslin.n11 (qables), 3 q.eslin.n12 (qables), 3 q.eslin.n13 (qables), 3 q.eslin.n14 (qables), 3 q.eslin.n15 (qables), 3 q.eslin.n16 (qables), 3 q.eslin.n17 (qables), 3 q.eslin.n18 (qables), 3 q.eslin.n19 (qables), 3 q.eslin.n2 (qables), 3 q.eslin.n20 (qables), 3 q.eslin.n21 (qables), 3 q.eslin.n22 (qables), 3 q.eslin.n23 (qables), 3 q.eslin.n24 (qables), 3 q.eslin.n25 (qables), 3 8

9 INDEX 9 q.eslin.n26 (qables), 3 q.eslin.n27 (qables), 3 q.eslin.n28 (qables), 3 q.eslin.n29 (qables), 3 q.eslin.n3 (qables), 3 q.eslin.n30 (qables), 3 q.eslin.n31 (qables), 3 q.eslin.n32 (qables), 3 q.eslin.n33 (qables), 3 q.eslin.n34 (qables), 3 q.eslin.n35 (qables), 3 q.eslin.n36 (qables), 3 q.eslin.n37 (qables), 3 q.eslin.n38 (qables), 3 q.eslin.n39 (qables), 3 q.eslin.n4 (qables), 3 q.eslin.n40 (qables), 3 q.eslin.n41 (qables), 3 q.eslin.n42 (qables), 3 q.eslin.n43 (qables), 3 q.eslin.n44 (qables), 3 q.eslin.n45 (qables), 3 q.eslin.n46 (qables), 3 q.eslin.n47 (qables), 3 q.eslin.n48 (qables), 3 q.eslin.n49 (qables), 3 q.eslin.n5 (qables), 3 q.eslin.n50 (qables), 3 q.eslin.n6 (qables), 3 q.eslin.n7 (qables), 3 q.eslin.n8 (qables), 3 q.eslin.n9 (qables), 3 qables, 3 recursive.b, 4 es.gaplin, 2, 4, 7 es.gaplin.p, 2 es.gaplin., 2 es.lin, 3, 5, 6 es.lin.p, 3 es.lin., 3