{
  "_id": "6a2139e4cd65a98ecbd27b16",
  "Package": "nnspat",
  "Type": "Package",
  "Title": "Nearest Neighbor Methods for Spatial Patterns",
  "Version": "0.1.1",
  "Author": "Elvan Ceyhan",
  "Maintainer": "Elvan Ceyhan <elvanceyhan@gmail.com>",
  "Description": "Contains the functions for testing the spatial patterns\n(of segregation, spatial symmetry, association, disease\nclustering, species correspondence and reflexivity) based on\nnearest neighbor relations, especially using contingency tables\nsuch as nearest neighbor contingency tables (Ceyhan (2010)\n<doi:10.1007/s10651-008-0104-x> and Ceyhan (2017)\n<doi:10.1016/j.jkss.2016.10.002> and references therein),\nnearest neighbor symmetry contingency tables (Ceyhan (2014)\n<doi:10.1155/2014/698296>), species correspondence contingency\ntables and reflexivity contingency tables (Ceyhan (2018)\n<doi:10.2436/20.8080.02.72>) for two (or higher) dimensional\ndata. Also contains functions for generating patterns of\nsegregation, association, uniformity in a multi-class setting\n(Ceyhan (2014) <doi:10.1007/s00477-013-0824-9>), and various\nnon-random labeling patterns for disease clustering in two\ndimensional cases (Ceyhan (2014) <doi:10.1002/sim.6053>), and\nfor visualization of all these patterns for the two dimensional\ndata. The tests are usually (asymptotic) normal z-tests and\nchi-square tests.",
  "License": "GPL-2",
  "Encoding": "UTF-8",
  "LazyData": "TRUE",
  "RdMacros": "Rdpack",
  "RoxygenNote": "7.1.2",
  "Config/pak/sysreqs": "cmake libfreetype6-dev libglu1-mesa-dev make\ntexlive libicu-dev libpng-dev libuv1-dev libgl1-mesa-dev\nzlib1g-dev",
  "Repository": "https://elvanceyhan.r-universe.dev",
  "Date/Publication": "2022-09-02 15:17:43 UTC",
  "RemoteUrl": "https://github.com/elvanceyhan/nnspat",
  "RemoteRef": "HEAD",
  "RemoteSha": "7173ace6a902ac6be47a3f85f918601cfb40ecb2",
  "NeedsCompilation": "no",
  "Packaged": {
    "Date": "2026-06-04 08:34:38 UTC",
    "User": "root"
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  "_user": "elvanceyhan",
  "_type": "src",
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  "_created": "2026-06-04T08:34:38.000Z",
  "_published": "2026-06-04T08:40:03.913Z",
  "_distro": "noble",
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    "author": "elvanceyhan <elvanceyhan@gmail.com>",
    "committer": "elvanceyhan <elvanceyhan@gmail.com>",
    "message": "mild updates to meet the new KATEX tex compiler in CRAN\n",
    "time": 1662131863
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    "name": "Elvan Ceyhan",
    "email": "elvanceyhan@gmail.com",
    "login": "elvanceyhan",
    "description": "Associate professor at the Dept of Mathematics and Statistics of Auburn University. Research interests: machine learning , data science, network optimization",
    "uuid": 44879392
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      "role": "Imports"
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    {
      "package": "stats",
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    {
      "package": "graphics",
      "role": "Imports"
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    {
      "package": "pcds",
      "role": "Imports"
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    {
      "package": "Rdpack",
      "version": ">= 0.7",
      "role": "Imports"
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  "_userbio": {
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    "type": "user",
    "name": "Elvan Ceyhan",
    "description": "Associate professor at the Dept of Mathematics and Statistics of Auburn University. Research interests: machine learning , data science, network optimization"
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    "extra/citation.html",
    "extra/citation.json",
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    "extra/contents.json",
    "extra/nnspat.html",
    "extra/readme.html",
    "extra/readme.md",
    "manual.pdf"
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  "_homeurl": "https://github.com/elvanceyhan/nnspat",
  "_realowner": "elvanceyhan",
  "_cranurl": true,
  "_releases": [
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      "version": "0.1.0",
      "date": "2021-05-10"
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      "date": "2022-08-30"
    },
    {
      "version": "0.1.2",
      "date": "2023-12-19"
    }
  ],
  "_exports": [
    "aij.mat",
    "aij.nonzero",
    "aij.theta",
    "asycovTkTl",
    "asyvarTk",
    "base.class.spec",
    "base.class.spec.ct",
    "bvnorm.pdf",
    "cell.spec",
    "cell.spec.ct",
    "cell.spec.ss",
    "cell.spec.ss.ct",
    "cellsTij",
    "ceTk",
    "ceTkinv",
    "ceTrun",
    "class.spec",
    "class.spec.ct",
    "classirest",
    "col.sum",
    "correct.cf1",
    "correct.cf2",
    "cov.2cells",
    "cov.2cols",
    "cov.cell.col",
    "cov.nnct",
    "cov.nnsym",
    "cov.seg.coeff",
    "cov.tct",
    "cov.tct3",
    "cov.tctI",
    "cov.tctIII",
    "cov.tctIV",
    "covCiCj",
    "covNii",
    "covNii.ct",
    "covNijCk",
    "covNrow2col",
    "covTcomb",
    "covTkTl",
    "dist.std.data",
    "dist2full",
    "euc.dist",
    "EV.Nii",
    "EV.nnct",
    "EV.rct",
    "EV.Tcomb",
    "EV.tct",
    "EV.tctI",
    "EV.Tk",
    "EV.Tkaij",
    "EV.Tkinv",
    "EV.Trun",
    "exact.nnct",
    "exact.pval1s",
    "exact.pval2s",
    "ipd.mat",
    "ipd.mat.euc",
    "kNN",
    "kNNdist",
    "kNNdist2cl",
    "kthNNdist",
    "kthNNdist2cl",
    "lab.onevsrest",
    "mat2vec",
    "matrix.sqrt",
    "Ninv",
    "NN",
    "NN.class.spec",
    "NN.class.spec.ct",
    "nnct",
    "nnct.boot.dis",
    "nnct.cr1",
    "nnct.cr2",
    "nnct.sub",
    "NNdist",
    "NNdist2cl",
    "NNsub",
    "Nt.def",
    "Ntkl",
    "overall.nnct",
    "overall.nnct.ct",
    "overall.seg",
    "overall.seg.ct",
    "overall.tct",
    "overall.tct.ct",
    "pairwise.lab",
    "pick.min.max",
    "prob.nnct",
    "Pseg.coeff",
    "Pseg.ss",
    "Pseg.ss.ct",
    "QRval",
    "Qsym.ct",
    "Qsym.test",
    "Qval",
    "Qvec",
    "rassoc",
    "rassocC",
    "rassocG",
    "rassocI",
    "rassocU",
    "rct",
    "rdiag.clust",
    "rhor.clust",
    "rnonRL",
    "rnonRLI",
    "rnonRLII",
    "rnonRLIII",
    "rnonRLIV",
    "row.sum",
    "rrot.clust",
    "rseg",
    "rself.ref",
    "runif.circ",
    "Rval",
    "scct",
    "scct.ct",
    "seg.coeff",
    "seg.ind",
    "sharedNN",
    "sharedNNmc",
    "SkewTk",
    "Tcomb",
    "tct",
    "tocher.cor",
    "Tval",
    "var.nnct",
    "var.nnsym",
    "var.seg.coeff",
    "var.tct",
    "varNii",
    "varNii.ct",
    "varPseg.coeff",
    "varTk",
    "varTkaij",
    "varTkinv.sim",
    "varTrun",
    "varTrun.sim",
    "W3val",
    "W4val",
    "W5val",
    "Wmat",
    "Xsq.ceTk",
    "Xsq.nnref",
    "Xsq.nnref.ct",
    "Xsq.nnsym",
    "Xsq.nnsym.dx",
    "Xsq.nnsym.dx.ct",
    "Xsq.nnsym.ss",
    "Xsq.nnsym.ss.ct",
    "Xsq.seg.coeff",
    "Xsq.seg.coeff.ct",
    "Xsq.spec.cor",
    "Xsq.spec.cor.ct",
    "Zcell.nnct",
    "Zcell.nnct.2s",
    "Zcell.nnct.ct",
    "Zcell.nnct.ls",
    "Zcell.nnct.pval",
    "Zcell.nnct.rs",
    "Zcell.tct",
    "Zcell.tct.ct",
    "ZceTk",
    "Zdir.nnct",
    "Zdir.nnct.ct",
    "Zdir.nnct.ss",
    "Zdir.nnct.ss.ct",
    "Zmixed.nonref",
    "Zmixed.nonref.ct",
    "Znnref",
    "Znnref.ct",
    "Znnself",
    "Znnself.ct",
    "Znnself.sum",
    "Znnself.sum.ct",
    "Znnsym",
    "Znnsym.dx",
    "Znnsym.dx.ct",
    "Znnsym.ss",
    "Znnsym.ss.ct",
    "Znnsym2cl",
    "Znnsym2cl.dx",
    "Znnsym2cl.dx.ct",
    "Znnsym2cl.ss",
    "Znnsym2cl.ss.ct",
    "Zseg.coeff",
    "Zseg.coeff.ct",
    "Zseg.ind",
    "Zseg.ind.ct",
    "Zself.ref",
    "Zself.ref.ct",
    "ZTcomb",
    "ZTkinv",
    "ZTkinv.sim",
    "ZTrun"
  ],
  "_datasets": [
    {
      "name": "swamptrees",
      "title": "Tree Species in a Swamp Forest",
      "object": "swamptrees",
      "class": [
        "data.frame"
      ],
      "fields": [
        "x",
        "y",
        "live",
        "sp"
      ],
      "rows": 734,
      "table": true,
      "tojson": true
    }
  ],
  "_help": [
    {
      "page": "dot-onAttach",
      "title": ".onAttach start message",
      "topics": [
        ".onAttach"
      ]
    },
    {
      "page": "dot-onLoad",
      "title": ".onLoad getOption package settings",
      "topics": [
        ".onLoad"
      ]
    },
    {
      "page": "aij.theta",
      "title": "Closeness or Proximity Matrix for Tango's Spatial Clustering Tests",
      "topics": [
        "aij.theta"
      ]
    },
    {
      "page": "asycovTkTl",
      "title": "Asymptotic Covariance between T_k and T_l Values",
      "topics": [
        "asycovTkTl"
      ]
    },
    {
      "page": "asyvarTk",
      "title": "Asymptotic Variance of Cuzick and Edwards T_k Test statistic",
      "topics": [
        "asyvarTk"
      ]
    },
    {
      "page": "bvnorm.pdf",
      "title": "pdf of the Bivariate Normal Distribution",
      "topics": [
        "bvnorm.pdf"
      ]
    },
    {
      "page": "cellsTij",
      "title": "Entries for the Types I-IV cell-specific tests",
      "topics": [
        "cellsTij"
      ]
    },
    {
      "page": "ceTk",
      "title": "Cuzick and Edwards T_k Test statistic",
      "topics": [
        "ceTk"
      ]
    },
    {
      "page": "ceTkinv",
      "title": "Cuzick and Edwards T_k^{inv} Test statistic",
      "topics": [
        "ceTkinv"
      ]
    },
    {
      "page": "ceTrun",
      "title": "Cuzick and Edwards T_{run} Test statistic",
      "topics": [
        "ceTrun"
      ]
    },
    {
      "page": "cov.nnct",
      "title": "Covariance Matrix of the Cell Counts in an NNCT",
      "topics": [
        "cov.nnct"
      ]
    },
    {
      "page": "cov.nnsym",
      "title": "Covariance Matrix of the Differences of the Off-Diagonal Cell Counts in an NNCT",
      "topics": [
        "cov.nnsym"
      ]
    },
    {
      "page": "cov.seg.coeff",
      "title": "Covariance Matrix of Segregation Coefficients in a Multi-class Case",
      "topics": [
        "cov.seg.coeff"
      ]
    },
    {
      "page": "cov.tct",
      "title": "Covariance Matrix of the Entries of the Type I-IV TCTs",
      "topics": [
        "cov.tct"
      ]
    },
    {
      "page": "covNrow2col",
      "title": "Conversion of the Covariance Matrix of the Row-wise Vectorized Cell Counts to Column-wise Vectorized Cell Counts in an NNCT",
      "topics": [
        "covNrow2col"
      ]
    },
    {
      "page": "covTcomb",
      "title": "Covariance matrix for T_k values in 'Tcomb'",
      "topics": [
        "covTcomb"
      ]
    },
    {
      "page": "covTkTl",
      "title": "Finite Sample Covariance between T_k and T_l Values",
      "topics": [
        "covTkTl"
      ]
    },
    {
      "page": "dist.std.data",
      "title": "Interpoint Distance Matrix for Standardized Data",
      "topics": [
        "dist.std.data"
      ]
    },
    {
      "page": "dist2full",
      "title": "Converts a lower triangular distance matrix to a full distance matrix",
      "topics": [
        "dist2full"
      ]
    },
    {
      "page": "euc.dist",
      "title": "The Euclidean distance between two vectors, matrices, or data frames",
      "topics": [
        "euc.dist"
      ]
    },
    {
      "page": "EV.Nii",
      "title": "Expected Values of the Self Entries in a Species Correspondence Contingency Table (SCCT)",
      "topics": [
        "EV.Nii"
      ]
    },
    {
      "page": "EV.nnct",
      "title": "Expected Values of the Cell Counts in NNCT",
      "topics": [
        "EV.nnct"
      ]
    },
    {
      "page": "EV.rct",
      "title": "Expected Values of the Cell Counts in RCT",
      "topics": [
        "EV.rct"
      ]
    },
    {
      "page": "EV.Tcomb",
      "title": "Expected Value for Cuzick & Edwards T_{comb} Test Statistic",
      "topics": [
        "EV.Tcomb"
      ]
    },
    {
      "page": "EV.tct",
      "title": "Expected Values of the Types I-IV cell-specific tests",
      "topics": [
        "EV.tct"
      ]
    },
    {
      "page": "EV.tctI",
      "title": "Expected Values of the Type I cell-specific tests",
      "topics": [
        "EV.tctI"
      ]
    },
    {
      "page": "EV.Tkinv",
      "title": "Expected Value of Cuzick and Edwards T_k^{inv} Test statistic",
      "topics": [
        "EV.Tkinv"
      ]
    },
    {
      "page": "exact.nnct",
      "title": "Exact version of Pearson's chi-square test on NNCTs",
      "topics": [
        "exact.nnct"
      ]
    },
    {
      "page": "exact.pval1s",
      "title": "p-value correction to the one-sided version of exact NNCT test",
      "topics": [
        "exact.pval1s"
      ]
    },
    {
      "page": "exact.pval2s",
      "title": "p-value correction to the two-sided version of exact NNCT test",
      "topics": [
        "exact.pval2s"
      ]
    },
    {
      "page": "funs.auxcovtct",
      "title": "Auxiliary Functions for Computing Covariances Between Cell Counts in the TCT",
      "topics": [
        "cov.2cells",
        "cov.2cols",
        "cov.cell.col",
        "covCiCj",
        "covNijCk",
        "funs.auxcovtct"
      ]
    },
    {
      "page": "funs.base.class.spec",
      "title": "Base Class-specific Chi-square Tests based on NNCTs",
      "topics": [
        "base.class.spec",
        "base.class.spec.ct",
        "funs.base.class.spec"
      ]
    },
    {
      "page": "funs.cell.spec.ss",
      "title": "Pielou's Cell-specific Segregation Test with Normal Approximation (for Sparse Sampling)",
      "topics": [
        "cell.spec.ss",
        "cell.spec.ss.ct",
        "funs.cell.spec.ss"
      ]
    },
    {
      "page": "funs.class.spec",
      "title": "Class-specific Chi-square Tests based on NNCTs",
      "topics": [
        "class.spec",
        "class.spec.ct",
        "funs.class.spec"
      ]
    },
    {
      "page": "funs.covNii",
      "title": "Covariance Matrix of the Self Entries in a Species Correspondence Contingency Table (SCCT)",
      "topics": [
        "covNii",
        "covNii.ct",
        "funs.covNii"
      ]
    },
    {
      "page": "funs.covtct",
      "title": "Functions for Covariances of the Entries of the Types I, III and IV TCTs",
      "topics": [
        "cov.tct3",
        "cov.tctI",
        "cov.tctIII",
        "cov.tctIV",
        "funs.covtct"
      ]
    },
    {
      "page": "funs.kNNdist",
      "title": "Functions for the k^{th} and 'k' NN distances",
      "topics": [
        "funs.kNNdist",
        "kNNdist",
        "kthNNdist"
      ]
    },
    {
      "page": "funs.kNNdist2cl",
      "title": "Functions for the k^{th} and 'k' NN distances",
      "topics": [
        "funs.kNNdist2cl",
        "kNNdist2cl",
        "kthNNdist2cl"
      ]
    },
    {
      "page": "funs.overall.nnct",
      "title": "Dixon's Overall Test of Segregation for NNCT",
      "topics": [
        "funs.overall.nnct",
        "overall.nnct",
        "overall.nnct.ct"
      ]
    },
    {
      "page": "funs.overall.seg",
      "title": "Overall Segregation Tests for NNCTs",
      "topics": [
        "funs.overall.seg",
        "overall.seg",
        "overall.seg.ct"
      ]
    },
    {
      "page": "funs.overall.tct",
      "title": "Types I-IV Overall Tests of Segregation for NNCT",
      "topics": [
        "funs.overall.tct",
        "overall.tct",
        "overall.tct.ct"
      ]
    },
    {
      "page": "funs.pijPij",
      "title": "The functions for probability of selecting a number of points from respective classes",
      "topics": [
        "funs.pijPij",
        "P11",
        "p11",
        "P111",
        "p111",
        "P1111",
        "p1111",
        "P1112",
        "p1112",
        "P112",
        "p112",
        "P1122",
        "p1122",
        "P1123",
        "p1123",
        "P12",
        "p12",
        "p122",
        "p1223",
        "P123",
        "p123",
        "P1234",
        "p1234"
      ]
    },
    {
      "page": "funs.scct",
      "title": "Species Correspondence Contingency Table (SCCT)",
      "topics": [
        "funs.scct",
        "scct",
        "scct.ct"
      ]
    },
    {
      "page": "funs.seg.coeff",
      "title": "Pielou's Segregation Coefficients for NNCTs",
      "topics": [
        "funs.seg.coeff",
        "Pseg.coeff",
        "seg.coeff"
      ]
    },
    {
      "page": "funs.varNii",
      "title": "Variances of the Self Entries in a Species Correspondence Contingency Table (SCCT)",
      "topics": [
        "funs.varNii",
        "varNii",
        "varNii.ct"
      ]
    },
    {
      "page": "funs.vartct",
      "title": "Functions for Variances of Cell Counts in the Types I, III and IV TCTs",
      "topics": [
        "funs.vartct",
        "var.tctI",
        "var.tctIII",
        "var.tctIV"
      ]
    },
    {
      "page": "funsAijmat",
      "title": "Aij matrices for computation of Moments of Cuzick and Edwards T_k Test statistic",
      "topics": [
        "aij.mat",
        "aij.nonzero",
        "funsAijmat"
      ]
    },
    {
      "page": "funsC_MI_II",
      "title": "Correction Matrices for the Covariance Matrix of NNCT entries",
      "topics": [
        "correct.cf1",
        "correct.cf2",
        "funsC_MI_II"
      ]
    },
    {
      "page": "funsExpTk",
      "title": "Expected Value for Cuzick and Edwards T_k Test statistic",
      "topics": [
        "EV.Tk",
        "EV.Tkaij",
        "funsExpTk"
      ]
    },
    {
      "page": "funsExpTrun",
      "title": "Expected Value for Cuzick and Edwards T_{run} Test statistic",
      "topics": [
        "EV.Trun",
        "EV.Trun.alt",
        "funsExpTrun"
      ]
    },
    {
      "page": "funsN_I_II",
      "title": "Correction Matrices for the NNCT entries",
      "topics": [
        "funsN_I_II",
        "nnct.cr1",
        "nnct.cr2"
      ]
    },
    {
      "page": "funsNNclass.spec",
      "title": "NN Class-specific Chi-square Tests based on NNCTs",
      "topics": [
        "funsNNclass.spec",
        "NN.class.spec",
        "NN.class.spec.ct"
      ]
    },
    {
      "page": "funsOnevsRest",
      "title": "Functions for one versus rest type labeling",
      "topics": [
        "classirest",
        "funsOnevsRest",
        "lab.onevsrest"
      ]
    },
    {
      "page": "funsPseg.ss",
      "title": "Pielou's Overall Test of Segregation for NNCT (for Sparse Sampling)",
      "topics": [
        "funsPseg.ss",
        "Pseg.ss",
        "Pseg.ss.ct"
      ]
    },
    {
      "page": "funsQandR",
      "title": "Functions for the Number of Shared NNs, Shared NN vector and the number of reflexive NNs",
      "topics": [
        "funsQandR",
        "Qval",
        "Qvec",
        "Rval",
        "sharedNN"
      ]
    },
    {
      "page": "funsRowColSums",
      "title": "Functions for row and column sums of a matrix",
      "topics": [
        "col.sum",
        "funsRowColSums",
        "row.sum"
      ]
    },
    {
      "page": "funsVarTk",
      "title": "Variance of Cuzick and Edwards T_k Test statistic",
      "topics": [
        "funsVarTk",
        "varTk",
        "varTkaij"
      ]
    },
    {
      "page": "funsVarTrun",
      "title": "Variance of Cuzick and Edwards T_{run} Test statistic",
      "topics": [
        "funsVarTrun",
        "varTrun",
        "varTrun.sim"
      ]
    },
    {
      "page": "funsW345values",
      "title": "W_k values for Tango's T test statistic",
      "topics": [
        "funsW345values",
        "W3val",
        "W4val",
        "W5val"
      ]
    },
    {
      "page": "funsXsq.nnref",
      "title": "Reflexivity Test with Chi-square Approximation",
      "topics": [
        "funsXsq.nnref",
        "Xsq.nnref",
        "Xsq.nnref.ct"
      ]
    },
    {
      "page": "funsXsq.nnsym.dx",
      "title": "Dixon's NN Symmetry Test with Chi-square Approximation for multiple classes",
      "topics": [
        "funsXsq.nnsym.dx",
        "Xsq.nnsym.dx",
        "Xsq.nnsym.dx.ct"
      ]
    },
    {
      "page": "funsXsq.nnsym.ss",
      "title": "Pielou's First Type of NN Symmetry Test with Chi-square Approximation for multiple classes (for Sparse Sampling)",
      "topics": [
        "funsXsq.nnsym.ss",
        "Xsq.nnsym.ss",
        "Xsq.nnsym.ss.ct"
      ]
    },
    {
      "page": "funsXsq.seg.coeff",
      "title": "Chi-square Test for Segregation Coefficients",
      "topics": [
        "funsXsq.seg.coeff",
        "Xsq.seg.coeff",
        "Xsq.seg.coeff.ct"
      ]
    },
    {
      "page": "funsXsq.spec.cor",
      "title": "Overall Species Correspondence Test with Chi-square Approximation",
      "topics": [
        "funsXsq.spec.cor",
        "Xsq.spec.cor",
        "Xsq.spec.cor.ct"
      ]
    },
    {
      "page": "funsZcell.nnct",
      "title": "Dixon's Cell-specific Z Tests of Segregation for NNCT",
      "topics": [
        "funsZcell.nnct",
        "Zcell.nnct",
        "Zcell.nnct.ct"
      ]
    },
    {
      "page": "funsZcell.nnct.pval",
      "title": "p-values for Cell-specific Z Test Statistics for NNCT",
      "topics": [
        "funsZcell.nnct.pval",
        "Zcell.nnct.2s",
        "Zcell.nnct.ls",
        "Zcell.nnct.pval",
        "Zcell.nnct.rs"
      ]
    },
    {
      "page": "funsZcell.spec",
      "title": "Cell-specific Z Tests of Segregation for NNCTs",
      "topics": [
        "cell.spec",
        "cell.spec.ct",
        "funsZcell.spec"
      ]
    },
    {
      "page": "funsZcell.tct",
      "title": "Types I-IV Cell-specific Z Tests of Segregation based on NNCTs",
      "topics": [
        "funsZcell.tct",
        "Zcell.tct",
        "Zcell.tct.ct"
      ]
    },
    {
      "page": "funsZdir.nnct",
      "title": "Directional Segregation Test for Two Classes with Normal Approximation",
      "topics": [
        "funsZdir.nnct",
        "Zdir.nnct",
        "Zdir.nnct.ct"
      ]
    },
    {
      "page": "funsZdir.nnct.ss",
      "title": "Directional Segregation Test for Two Classes with Normal Approximation (for Sparse Sampling)",
      "topics": [
        "funsZdir.nnct.ss",
        "Zdir.nnct.ss",
        "Zdir.nnct.ss.ct"
      ]
    },
    {
      "page": "funsZmixed.nonref",
      "title": "Mixed-Non-Reflexivity Test with Normal Approximation",
      "topics": [
        "funsZmixed.nonref",
        "Zmixed.nonref",
        "Zmixed.nonref.ct"
      ]
    },
    {
      "page": "funsZnnref",
      "title": "Z Tests for NN Reflexivity",
      "topics": [
        "funsZnnref",
        "Znnref",
        "Znnref.ct"
      ]
    },
    {
      "page": "funsZnnself",
      "title": "Self-Reflexivity Tests with Normal Approximation",
      "topics": [
        "funsZnnself",
        "Znnself",
        "Znnself.ct"
      ]
    },
    {
      "page": "funsZnnself.sum",
      "title": "Cumulative Species Correspondence Test with Normal Approximation",
      "topics": [
        "funsZnnself.sum",
        "Znnself.sum",
        "Znnself.sum.ct"
      ]
    },
    {
      "page": "funsZnnsym.dx",
      "title": "Dixon's Pairwise NN Symmetry Test with Normal Approximation",
      "topics": [
        "funsZnnsym.dx",
        "Znnsym.dx",
        "Znnsym.dx.ct"
      ]
    },
    {
      "page": "funsZnnsym.ss",
      "title": "Pielou's Pairwise NN Symmetry Test with Normal Approximation (for Sparse Sampling)",
      "topics": [
        "funsZnnsym.ss",
        "Znnsym.ss",
        "Znnsym.ss.ct"
      ]
    },
    {
      "page": "funsZnnsym2cl.dx",
      "title": "Dixon's NN Symmetry Test with Normal Approximation for Two Classes",
      "topics": [
        "funsZnnsym2cl.dx",
        "Znnsym2cl.dx",
        "Znnsym2cl.dx.ct"
      ]
    },
    {
      "page": "funsZnnsym2cl.ss",
      "title": "Pielou's First Type of NN Symmetry Test with Normal Approximation for Two Classes (for Sparse Sampling)",
      "topics": [
        "funsZnnsym2cl.ss",
        "Znnsym2cl.ss",
        "Znnsym2cl.ss.ct"
      ]
    },
    {
      "page": "funsZseg.coeff",
      "title": "Z Tests for Segregation Coefficients",
      "topics": [
        "funsZseg.coeff",
        "Zseg.coeff",
        "Zseg.coeff.ct"
      ]
    },
    {
      "page": "funsZsegind",
      "title": "Z Tests for Segregation Indices",
      "topics": [
        "funsZsegind",
        "Zseg.ind",
        "Zseg.ind.ct"
      ]
    },
    {
      "page": "funsZself.ref",
      "title": "Self-Reflexivity Test with Normal Approximation",
      "topics": [
        "funsZself.ref",
        "Zself.ref",
        "Zself.ref.ct"
      ]
    },
    {
      "page": "funsZTkinv",
      "title": "Z-Test for Cuzick and Edwards T_k^{inv} statistic",
      "topics": [
        "funsZTkinv",
        "ZTkinv",
        "ZTkinv.sim"
      ]
    },
    {
      "page": "ind.nnsym",
      "title": "Index Matrix for Computing the Covariance of Dixon's Overall NN Symmetry Test",
      "topics": [
        "ind.nnsym"
      ]
    },
    {
      "page": "ind.seg.coeff",
      "title": "Index Matrix for Computing the Covariance of Segregation Coefficients",
      "topics": [
        "ind.seg.coeff"
      ]
    },
    {
      "page": "ipd.mat",
      "title": "Interpoint Distance Matrix",
      "topics": [
        "ipd.mat"
      ]
    },
    {
      "page": "ipd.mat.euc",
      "title": "Euclidean Interpoint Distance Matrix",
      "topics": [
        "ipd.mat.euc"
      ]
    },
    {
      "page": "kNN",
      "title": "Finding the indices of the 'k' NNs of a given point",
      "topics": [
        "kNN"
      ]
    },
    {
      "page": "mat2vec",
      "title": "Conversion of a Matrix to a Vector",
      "topics": [
        "mat2vec"
      ]
    },
    {
      "page": "matrix.sqrt",
      "title": "Square root of a matrix",
      "topics": [
        "matrix.sqrt"
      ]
    },
    {
      "page": "Ninv",
      "title": "Vector of Shared NNs and Number of Reflexive NNs",
      "topics": [
        "Ninv"
      ]
    },
    {
      "page": "NN",
      "title": "Finding the index of the NN of a given point",
      "topics": [
        "NN"
      ]
    },
    {
      "page": "nnct",
      "title": "Nearest Neighbor Contingency Table (NNCT)",
      "topics": [
        "nnct"
      ]
    },
    {
      "page": "nnct.boot.dis",
      "title": "Bootstrap Nearest Neighbor Contingency Table (NNCT)",
      "topics": [
        "nnct.boot.dis"
      ]
    },
    {
      "page": "nnct.sub",
      "title": "Nearest Neighbor Contingency Table (NNCT) with (only) base points restricted to a subsample",
      "topics": [
        "nnct.sub"
      ]
    },
    {
      "page": "NNdist",
      "title": "Distances between subjects and their NNs",
      "topics": [
        "NNdist"
      ]
    },
    {
      "page": "NNdist2cl",
      "title": "Distances between subjects from class i and their NNs from class j",
      "topics": [
        "NNdist2cl"
      ]
    },
    {
      "page": "nnspat",
      "title": "nnspat: A package for NN Methods and Their Use in Testing Spatial Patterns",
      "topics": [
        "nnspat"
      ]
    },
    {
      "page": "NNsub",
      "title": "Finding the index of the NN of a given point among a subset of points",
      "topics": [
        "NNsub"
      ]
    },
    {
      "page": "Nt.def",
      "title": "N_t Value (found with the definition formula)",
      "topics": [
        "Nt.def"
      ]
    },
    {
      "page": "Ntkl",
      "title": "N_{tkl} Value",
      "topics": [
        "Ntkl"
      ]
    },
    {
      "page": "pairwise.lab",
      "title": "Keeping the pair of the specified labels in the data",
      "topics": [
        "pairwise.lab"
      ]
    },
    {
      "page": "pick.min.max",
      "title": "Smallest and Largest Distances in a Distance Matrix",
      "topics": [
        "pick.min.max"
      ]
    },
    {
      "page": "pk",
      "title": "Probability of 'k' items selected from the class with size n_1",
      "topics": [
        "pk"
      ]
    },
    {
      "page": "plot.Clusters",
      "title": "Plot a 'Clusters' object",
      "topics": [
        "plot.Clusters"
      ]
    },
    {
      "page": "plot.SpatPatterns",
      "title": "Plot a 'SpatPatterns' object",
      "topics": [
        "plot.SpatPatterns"
      ]
    },
    {
      "page": "print.cellhtest",
      "title": "Print a summary of a 'cellhtest' object",
      "topics": [
        "print.cellhtest"
      ]
    },
    {
      "page": "print.Chisqtest",
      "title": "Print a summary of a 'Chisqtest' object",
      "topics": [
        "print.Chisqtest"
      ]
    },
    {
      "page": "print.classhtest",
      "title": "Print a summary of a 'classhtest' object",
      "topics": [
        "print.classhtest"
      ]
    },
    {
      "page": "print.Clusters",
      "title": "Print a 'Clusters' object",
      "topics": [
        "print.Clusters"
      ]
    },
    {
      "page": "print.refhtest",
      "title": "Print a summary of a 'refhtest' object",
      "topics": [
        "print.refhtest"
      ]
    },
    {
      "page": "print.SpatPatterns",
      "title": "Print a 'SpatPatterns' object",
      "topics": [
        "print.SpatPatterns"
      ]
    },
    {
      "page": "print.summary.Clusters",
      "title": "Print a summary of a 'Clusters' object",
      "topics": [
        "print.summary.Clusters"
      ]
    },
    {
      "page": "print.summary.SpatPatterns",
      "title": "Print a summary of a 'SpatPatterns' object",
      "topics": [
        "print.summary.SpatPatterns"
      ]
    },
    {
      "page": "prob.nnct",
      "title": "Probability of the current nearest neighbor contingency table",
      "topics": [
        "prob.nnct"
      ]
    },
    {
      "page": "QRval",
      "title": "Number of Shared and Reflexive NNs",
      "topics": [
        "QRval"
      ]
    },
    {
      "page": "Qsym.ct",
      "title": "Q-symmetry Contingency Table (QCT)",
      "topics": [
        "Qsym.ct"
      ]
    },
    {
      "page": "Qsym.test",
      "title": "Pielou's Second Type of NN Symmetry Test with Chi-square Approximation",
      "topics": [
        "Qsym.test"
      ]
    },
    {
      "page": "rassoc",
      "title": "Generation of Points Associated with a Given Set of Points",
      "topics": [
        "rassoc"
      ]
    },
    {
      "page": "rassocC",
      "title": "Generation of Points Associated in the Type C Sense with a Given Set of Points",
      "topics": [
        "rassocC"
      ]
    },
    {
      "page": "rassocG",
      "title": "Generation of Points Associated in the Type G Sense with a Given Set of Points",
      "topics": [
        "rassocG"
      ]
    },
    {
      "page": "rassocI",
      "title": "Generation of Points Associated in the Type I Sense with a Given Set of Points",
      "topics": [
        "rassocI"
      ]
    },
    {
      "page": "rassocU",
      "title": "Generation of Points Associated in the Type U Sense with a Given Set of Points",
      "topics": [
        "rassocU"
      ]
    },
    {
      "page": "rct",
      "title": "Reflexivity Contingency Table (RCT)",
      "topics": [
        "rct"
      ]
    },
    {
      "page": "rdiag.clust",
      "title": "Generation of Points with Clusters along the First Diagonal",
      "topics": [
        "rdiag.clust"
      ]
    },
    {
      "page": "rhor.clust",
      "title": "Generation of Points with Clusters along the Horizontal Axis",
      "topics": [
        "rhor.clust"
      ]
    },
    {
      "page": "rnonRL",
      "title": "Non-Random Labeling of a Given Set of Points",
      "topics": [
        "rnonRL"
      ]
    },
    {
      "page": "rnonRLI",
      "title": "Type I Non-Random Labeling of a Given Set of Points",
      "topics": [
        "rnonRLI"
      ]
    },
    {
      "page": "rnonRLII",
      "title": "Type II Non-Random Labeling of a Given Set of Points",
      "topics": [
        "rnonRLII"
      ]
    },
    {
      "page": "rnonRLIII",
      "title": "Type III Non-Random Labeling of a Given Set of Points",
      "topics": [
        "rnonRLIII"
      ]
    },
    {
      "page": "rnonRLIV",
      "title": "Type IV Non-Random Labeling of a Given Set of Points",
      "topics": [
        "rnonRLIV"
      ]
    },
    {
      "page": "rrot.clust",
      "title": "Generation of Points with Rotational Clusters",
      "topics": [
        "rrot.clust"
      ]
    },
    {
      "page": "rseg",
      "title": "Generation of Points under Segregation of Two Classes",
      "topics": [
        "rseg"
      ]
    },
    {
      "page": "rself.ref",
      "title": "Generation of Points from Self Correspondence Pattern",
      "topics": [
        "rself.ref"
      ]
    },
    {
      "page": "runif.circ",
      "title": "Generation of Uniform Points in a Circle",
      "topics": [
        "runif.circ"
      ]
    },
    {
      "page": "seg.ind",
      "title": "Dixon's Segregation Indices for NNCTs",
      "topics": [
        "seg.ind"
      ]
    },
    {
      "page": "sharedNNmc",
      "title": "The Shared NN Vectors for Multiple Classes",
      "topics": [
        "sharedNNmc"
      ]
    },
    {
      "page": "SkewTk",
      "title": "Skewness of Cuzick and Edwards T_k Test statistic",
      "topics": [
        "SkewTk"
      ]
    },
    {
      "page": "summary.Clusters",
      "title": "Return a summary of a 'Clusters' object",
      "topics": [
        "summary.Clusters"
      ]
    },
    {
      "page": "summary.SpatPatterns",
      "title": "Return a summary of a 'SpatPatterns' object",
      "topics": [
        "summary.SpatPatterns"
      ]
    },
    {
      "page": "swamptrees",
      "title": "Tree Species in a Swamp Forest",
      "topics": [
        "swamptrees"
      ]
    },
    {
      "page": "Tcomb",
      "title": "Cuzick & Edwards Tcomb Test Statistic",
      "topics": [
        "Tcomb"
      ]
    },
    {
      "page": "tct",
      "title": "T Contingency Table (TCT)",
      "topics": [
        "tct"
      ]
    },
    {
      "page": "tocher.cor",
      "title": "Tocher's randomized correction to the exact p-value",
      "topics": [
        "tocher.cor"
      ]
    },
    {
      "page": "Tval",
      "title": "T value in NN structure",
      "topics": [
        "Tval"
      ]
    },
    {
      "page": "var.nnct",
      "title": "Variances of Cell Counts in an NNCT",
      "topics": [
        "var.nnct"
      ]
    },
    {
      "page": "var.nnsym",
      "title": "Variances of Differences of Off-Diagonal Entries in an NNCT",
      "topics": [
        "var.nnsym"
      ]
    },
    {
      "page": "var.seg.coeff",
      "title": "Variances of Segregation Coefficients in a Multi-class Case",
      "topics": [
        "var.seg.coeff"
      ]
    },
    {
      "page": "var.tct",
      "title": "Variances of Entries in a TCT",
      "topics": [
        "var.tct"
      ]
    },
    {
      "page": "varPseg.coeff",
      "title": "Variance of Pielou's Segregation Coefficient for 2 Classes",
      "topics": [
        "varPseg.coeff"
      ]
    },
    {
      "page": "varTkinv.sim",
      "title": "Simulated Variance of Cuzick and Edwards T_k^{inv} Test statistic",
      "topics": [
        "varTkinv.sim"
      ]
    },
    {
      "page": "Wmat",
      "title": "The incidence matrix 'W' for the NN digraph",
      "topics": [
        "Wmat"
      ]
    },
    {
      "page": "Xsq.ceTk",
      "title": "Chi-square Approximation to Cuzick and Edwards T_k Test statistic",
      "topics": [
        "Xsq.ceTk"
      ]
    },
    {
      "page": "Xsq.nnsym",
      "title": "Overall NN Symmetry Test with Chi-square Approximation",
      "topics": [
        "Xsq.nnsym"
      ]
    },
    {
      "page": "ZceTk",
      "title": "Z-test for Cuzick and Edwards T_k statistic",
      "topics": [
        "ZceTk"
      ]
    },
    {
      "page": "Znnsym",
      "title": "NN Symmetry Test with Normal Approximation",
      "topics": [
        "Znnsym"
      ]
    },
    {
      "page": "Znnsym2cl",
      "title": "NN Symmetry Test with Normal Approximation for Two Classes",
      "topics": [
        "Znnsym2cl"
      ]
    },
    {
      "page": "ZTcomb",
      "title": "Z-test for Cuzick and Edwards T_{comb} statistic",
      "topics": [
        "ZTcomb"
      ]
    },
    {
      "page": "ZTrun",
      "title": "Z-test for Cuzick and Edwards T_{run} statistic",
      "topics": [
        "ZTrun"
      ]
    }
  ],
  "_readme": "https://github.com/elvanceyhan/nnspat/raw/HEAD/README.md",
  "_rundeps": [
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    "base64enc",
    "bslib",
    "cachem",
    "cli",
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    "cpp11",
    "deldir",
    "digest",
    "dplyr",
    "evaluate",
    "farver",
    "fastmap",
    "fontawesome",
    "fs",
    "generics",
    "geometry",
    "ggplot2",
    "ggrepel",
    "glue",
    "gMOIP",
    "gtable",
    "highr",
    "htmltools",
    "htmlwidgets",
    "interp",
    "isoband",
    "jquerylib",
    "jsonlite",
    "knitr",
    "labeling",
    "lattice",
    "lifecycle",
    "linprog",
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