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  "Title": "Arc-Length Statistics: Goodness of Fit, Distributions and a\nBayesian Test",
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  "Authors@R": "person(\"M. Theodor\", \"Loots\", role = c(\"aut\", \"cre\"), email = \"theo.loots@gmail.com\",\ncomment = c(ORCID = \"0000-0001-7722-3913\"))",
  "Description": "Inference from the arc length of statistical functions.\nThree tools share one pure-C back-end: a goodness-of-fit test\nbased on the arc length of the probability plot, with an\nanalytic saddlepoint null and sensitivity to local density\nstructure that the empirical-distribution tests miss; two\nconstructions that build a distribution from the arc length of\nits defining curve, the arc-length generator and the quantile\narc-length family estimated by L-moments; and a Bayesian\nnonparametric arc-length goodness-of-fit test on the\nDirichlet-process posterior. The same C sources back the\n'Python' package 'arcstat'.",
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  "BugReports": "https://github.com/mtloots/arcstat/issues",
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  "Repository": "https://mtloots.r-universe.dev",
  "Date/Publication": "2026-10-12 06:41:19 UTC",
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  "Author": "M. Theodor Loots [aut, cre] (ORCID:\n<https://orcid.org/0000-0001-7722-3913>)",
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    "message": "arcstat 0.3.1: clamp al_pvalue to [0, 1] on both fronts\n\nThe Lugannani-Rice tail overshoots far in the right tail and returned\n-6.5e-29 and -2.1e-89 on badly non-uniform samples at n = 150. Clamped in\nthe shared C back-end; the Python copy had not received the fix and is\nsynced here. Regression tests on both fronts. R CMD check --as-cran: 1\nNOTE (local HTML Tidy/V8 only). Python: 22 tests pass.\n\nCo-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>\nClaude-Session: https://claude.ai/code/session_01BndzHvPf3J85ySV2GrN7BW\n",
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  "_assets": [
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  "_exports": [
    "admiss_rho",
    "al_band_model",
    "al_band_model_star",
    "al_band_sample",
    "al_moments",
    "al_pvalue",
    "al_scale",
    "al_scale_raw",
    "al_statistic",
    "al_test",
    "arc_generator",
    "arcc_c3max",
    "arcc_exact_ci",
    "arcc_gof",
    "arccirc",
    "arccirc_fr",
    "arclength",
    "arcq",
    "bb_evidence",
    "bb_post_disc",
    "bb_ref_disc",
    "bc_cdf",
    "bc_pdf",
    "bc_q",
    "cf_arclength",
    "cf_arclength_family",
    "darccirc",
    "darccirc_fr",
    "darcq",
    "dgen",
    "dtemper_vm",
    "eq_bstar",
    "eq_E",
    "eq_E_sweep",
    "eq_readings",
    "eq_readings_vsl",
    "eq_ub_quad",
    "eqfit_bc",
    "eqfit_bc_boot",
    "eqfit_blocklen",
    "eqfit_estsim",
    "eqfit_k4eq",
    "eqfit_k4eq_boot",
    "eqfit_msim",
    "eqfit_nullT",
    "eqfit_score_at",
    "eqfit_taus",
    "factorise_rho",
    "fit_arccirc",
    "fit_arccirc_fr",
    "fit_arcq",
    "fit_arcq_cf",
    "k4_ab_sweep",
    "k4_b_sweep",
    "k4_band_model",
    "k4_band_sample",
    "k4_band_trop_mean",
    "k4_cdf",
    "k4_fit_aleq",
    "k4_fit_lmom",
    "k4_fit_nalr",
    "k4_fit_nls",
    "k4_fit_varpro",
    "k4_icc",
    "k4_locus_dist",
    "k4_mv_boot",
    "k4_pdf",
    "k4_q",
    "k4_readings",
    "k4_runmed",
    "k4_tau34",
    "lmom_circ",
    "lmoments",
    "lmratios",
    "parcq",
    "pgen",
    "Q_arccirc",
    "Q_arccirc_fr",
    "qarcq",
    "qd_arccirc",
    "qd_arccirc_fr",
    "qmin_rho",
    "rarccirc",
    "rarccirc_fr",
    "rarcq",
    "rgen",
    "rho_arccirc",
    "rho_from_lmom",
    "sample_lmoments",
    "trigmom_arccirc",
    "trigmom_arccirc_fr",
    "trigmom_temper_vm"
  ],
  "_help": [
    {
      "page": "al_band_model",
      "title": "Band arc length of the normal reference curve (C back-end)",
      "topics": [
        "al_band_model"
      ]
    },
    {
      "page": "al_band_model_star",
      "title": "Spacing-corrected model band arc length (C back-end)",
      "topics": [
        "al_band_model_star"
      ]
    },
    {
      "page": "al_band_sample",
      "title": "Sample band arc length of the empirical distribution curve (C back-end)",
      "topics": [
        "al_band_sample"
      ]
    },
    {
      "page": "al_moments",
      "title": "Exact mean, variance and support of the arc-length statistic (C back-end)",
      "topics": [
        "al_moments"
      ]
    },
    {
      "page": "al_pvalue",
      "title": "Saddlepoint right-tail probability of the arc-length statistic (C back-end)",
      "topics": [
        "al_pvalue"
      ]
    },
    {
      "page": "al_scale",
      "title": "Scale by arc-length band matching, in the scale-equivariant standardised form (C back-end)",
      "topics": [
        "al_scale"
      ]
    },
    {
      "page": "al_scale_raw",
      "title": "The uncorrected band-matching scale estimator (C back-end)",
      "topics": [
        "al_scale_raw"
      ]
    },
    {
      "page": "al_statistic",
      "title": "Arc-length goodness-of-fit statistic (C back-end)",
      "topics": [
        "al_statistic"
      ]
    },
    {
      "page": "al_test",
      "title": "Arc-length goodness-of-fit test",
      "topics": [
        "al_test"
      ]
    },
    {
      "page": "arc_generator",
      "title": "Arc-length generator: transform a bounded-support base into a new distribution",
      "topics": [
        "arc_generator",
        "dgen",
        "pgen",
        "rgen"
      ]
    },
    {
      "page": "arcc_c3max",
      "title": "Largest admissible shape parameter of the smooth circular family",
      "topics": [
        "arcc_c3max"
      ]
    },
    {
      "page": "arcc_exact_ci",
      "title": "Exact confidence interval for the shape parameter of the wrapped order-three family",
      "topics": [
        "arcc_exact_ci"
      ]
    },
    {
      "page": "arcc_gof",
      "title": "Goodness of fit of a fitted circular arc-length member",
      "topics": [
        "arcc_gof"
      ]
    },
    {
      "page": "arccirc",
      "title": "The smooth circular arc-length family",
      "topics": [
        "arccirc",
        "darccirc",
        "qd_arccirc",
        "Q_arccirc",
        "rarccirc",
        "rho_arccirc",
        "trigmom_arccirc"
      ]
    },
    {
      "page": "arccirc_fr",
      "title": "Fejer-Riesz form of the circular arc-length family",
      "topics": [
        "arccirc_fr",
        "darccirc_fr",
        "qd_arccirc_fr",
        "Q_arccirc_fr",
        "rarccirc_fr",
        "trigmom_arccirc_fr"
      ]
    },
    {
      "page": "arcq",
      "title": "Construct a quantile arc-length distribution",
      "topics": [
        "arclength",
        "arcq",
        "darcq",
        "parcq",
        "qarcq",
        "rarcq"
      ]
    },
    {
      "page": "bb_evidence",
      "title": "Bayesian arc-length goodness-of-fit evidence",
      "topics": [
        "bb_evidence"
      ]
    },
    {
      "page": "bb_post_disc",
      "title": "Bayesian-bootstrap posterior arc-length discrepancies",
      "topics": [
        "bb_post_disc"
      ]
    },
    {
      "page": "bb_ref_disc",
      "title": "Null reference distribution of the arc-length discrepancy",
      "topics": [
        "bb_ref_disc"
      ]
    },
    {
      "page": "bc_cdf",
      "title": "Beta-companion distribution function",
      "topics": [
        "bc_cdf"
      ]
    },
    {
      "page": "bc_pdf",
      "title": "Beta-companion density",
      "topics": [
        "bc_pdf"
      ]
    },
    {
      "page": "bc_q",
      "title": "Beta-companion quantile function (standardised support)",
      "topics": [
        "bc_q"
      ]
    },
    {
      "page": "cf_arclength",
      "title": "Arc length of the empirical characteristic function (C back-end)",
      "topics": [
        "cf_arclength"
      ]
    },
    {
      "page": "cf_arclength_family",
      "title": "Closed-form characteristic-function arc length for named families",
      "topics": [
        "cf_arclength_family"
      ]
    },
    {
      "page": "dtemper_vm",
      "title": "Arc-length tempering of a von Mises base",
      "topics": [
        "dtemper_vm",
        "trigmom_temper_vm"
      ]
    },
    {
      "page": "eq_bstar",
      "title": "Equivalence curve",
      "topics": [
        "eq_bstar"
      ]
    },
    {
      "page": "eq_E",
      "title": "Closed-form equivalence discrepancy",
      "topics": [
        "eq_E"
      ]
    },
    {
      "page": "eq_readings",
      "title": "Quantile-domain induction readings and equivalence discrepancy for tilted beta-kernel quantile densities q(u) = u^alpha (1-u)^beta exp(sum theta_j P_j(u))",
      "topics": [
        "eq_readings",
        "eq_readings_vsl"
      ]
    },
    {
      "page": "eq_ub_quad",
      "title": "Quadratic shoulder and mode of the kernel family",
      "topics": [
        "eq_ub_quad"
      ]
    },
    {
      "page": "eqfit_bc",
      "title": "The equivalence-system paper's fitting and simulation loops, in the back end",
      "topics": [
        "eqfit_bc",
        "eqfit_bc_boot",
        "eqfit_blocklen",
        "eqfit_estsim",
        "eqfit_k4eq",
        "eqfit_k4eq_boot",
        "eqfit_msim",
        "eqfit_nullT",
        "eqfit_score_at",
        "eqfit_taus",
        "eq_E_sweep",
        "k4_ab_sweep",
        "k4_b_sweep"
      ]
    },
    {
      "page": "fit_arccirc",
      "title": "Method-of-moments fit of the smooth circular arc-length family",
      "topics": [
        "fit_arccirc"
      ]
    },
    {
      "page": "fit_arccirc_fr",
      "title": "Closed-form fit of the Fejer-Riesz circular arc-length family",
      "topics": [
        "fit_arccirc_fr"
      ]
    },
    {
      "page": "fit_arcq",
      "title": "Fit an arcq distribution to data by matching L-moments",
      "topics": [
        "fit_arcq"
      ]
    },
    {
      "page": "fit_arcq_cf",
      "title": "Closed-form L-moment fit of the order-two arcq family",
      "topics": [
        "fit_arcq_cf"
      ]
    },
    {
      "page": "k4_band_model",
      "title": "Band arc lengths of a scaled kappa curve and of a data polyline",
      "topics": [
        "k4_band_model",
        "k4_band_sample"
      ]
    },
    {
      "page": "k4_band_trop_mean",
      "title": "Exact mean of the tropical band arc length under Gaussian error",
      "topics": [
        "k4_band_trop_mean"
      ]
    },
    {
      "page": "k4_fit_lmom",
      "title": "Deterministic kappa fits: L-moment shape inversion, quantile-domain arc-length shape fit, curve-domain NLS and NALR (banded arc lengths of the running-median presmoothed polyline)",
      "topics": [
        "k4_fit_aleq",
        "k4_fit_lmom",
        "k4_fit_nalr",
        "k4_fit_nls"
      ]
    },
    {
      "page": "k4_fit_varpro",
      "title": "Variable-projection fit of the drifted kappa response",
      "topics": [
        "k4_fit_varpro"
      ]
    },
    {
      "page": "k4_icc",
      "title": "One-way variance components and the intraclass correlation",
      "topics": [
        "k4_icc"
      ]
    },
    {
      "page": "k4_locus_dist",
      "title": "Distance from fitted shapes to the equivalence locus",
      "topics": [
        "k4_locus_dist"
      ]
    },
    {
      "page": "k4_mv_boot",
      "title": "The fitting-method multiverse of one induction run: eight admissible pipelines under one moving-block residual bootstrap",
      "topics": [
        "k4_mv_boot"
      ]
    },
    {
      "page": "k4_q",
      "title": "Four-parameter kappa quantile, distribution and density functions",
      "topics": [
        "k4_cdf",
        "k4_pdf",
        "k4_q"
      ]
    },
    {
      "page": "k4_readings",
      "title": "The two standard induction-period readings of a fitted kappa curve",
      "topics": [
        "k4_readings"
      ]
    },
    {
      "page": "k4_runmed",
      "title": "Running median with shrinking symmetric windows at the edges",
      "topics": [
        "k4_runmed"
      ]
    },
    {
      "page": "k4_tau34",
      "title": "Theoretical L-moment ratios of the standard kappa distribution",
      "topics": [
        "k4_tau34"
      ]
    },
    {
      "page": "lmom_circ",
      "title": "Circular L-moments",
      "topics": [
        "admiss_rho",
        "factorise_rho",
        "lmom_circ",
        "qmin_rho",
        "rho_from_lmom"
      ]
    },
    {
      "page": "lmoments",
      "title": "Theoretical L-moments of an arcq distribution",
      "topics": [
        "lmoments"
      ]
    },
    {
      "page": "lmratios",
      "title": "L-moment ratios (tau_3, tau_4, ...) from a vector of L-moments",
      "topics": [
        "lmratios"
      ]
    },
    {
      "page": "sample_lmoments",
      "title": "Sample L-moments of data",
      "topics": [
        "sample_lmoments"
      ]
    }
  ],
  "_readme": "https://github.com/mtloots/arcstat/raw/HEAD/arcstat/README.md",
  "_rundeps": [],
  "_sysdeps": [
    {
      "shlib": "libgomp",
      "package": "libgomp1",
      "source": "gcc",
      "version": "16-20260322-1ubuntu1",
      "name": "openmp",
      "homepage": "http://gcc.gnu.org/",
      "description": "GCC OpenMP (GOMP) support library"
    }
  ],
  "_vignettes": [
    {
      "source": "arcstat.Rmd",
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