Package: arcstat 0.3.1

arcstat: Arc-Length Statistics: Goodness of Fit, Distributions and a Bayesian Test

Inference from the arc length of statistical functions. Three tools share one pure-C back-end: a goodness-of-fit test based on the arc length of the probability plot, with an analytic saddlepoint null and sensitivity to local density structure that the empirical-distribution tests miss; two constructions that build a distribution from the arc length of its defining curve, the arc-length generator and the quantile arc-length family estimated by L-moments; and a Bayesian nonparametric arc-length goodness-of-fit test on the Dirichlet-process posterior. The same C sources back the 'Python' package 'arcstat'.

Authors:M. Theodor Loots [aut, cre]

arcstat_0.3.1.tar.gz
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arcstat_0.3.1.tgz(r-4.6-x86_64)arcstat_0.3.1.tgz(r-4.6-arm64)arcstat_0.3.1.tgz(r-4.5-x86_64)arcstat_0.3.1.tgz(r-4.5-arm64)
arcstat_0.3.1.tar.gz(r-4.7-arm64)arcstat_0.3.1.tar.gz(r-4.7-x86_64)arcstat_0.3.1.tar.gz(r-4.6-arm64)arcstat_0.3.1.tar.gz(r-4.6-x86_64)
arcstat_0.3.1.tgz(r-4.6-emscripten)
manual.pdf |manual.html✨
DESCRIPTION |NEWS
card.svg |card.png
arcstat/json (API)

# Install 'arcstat' in R:

install.packages('arcstat', repos = c('https://mtloots.r-universe.dev', 'https://cloud.r-project.org'))

Bug tracker:https://github.com/mtloots/arcstat/issues

Uses libs:

openmp– GCC OpenMP (GOMP) support library

On CRAN:

openmp

4.48 score 590 downloads 92 exports 0 dependencies

Last updated from:03640e5ff6. Checks:15 OK. Indexed: yes.

Target	Result	Time
linux-devel-arm64	OK	113
linux-devel-x86_64	OK	144
source / vignettes	OK	195
linux-release-arm64	OK	130
linux-release-x86_64	OK	183
macos-release-arm64	OK	229
macos-release-x86_64	OK	261
macos-oldrel-arm64	OK	199
macos-oldrel-x86_64	OK	317
windows-devel-arm64	OK	366
windows-devel-x86_64	OK	218
windows-release-arm64	OK	339
windows-release-x86_64	OK	178
windows-oldrel-x86_64	OK	136
wasm-release	OK	77

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

Dependencies:

Arc length as a statistical functional

Rendered fromarcstat.Rmdusingknitr::rmarkdown

Last update: 2026-08-10
Started: 2026-08-10

Help page	Topics
Band arc length of the normal reference curve (C back-end)	al_band_model
Spacing-corrected model band arc length (C back-end)	al_band_model_star
Sample band arc length of the empirical distribution curve (C back-end)	al_band_sample
Exact mean, variance and support of the arc-length statistic (C back-end)	al_moments
Saddlepoint right-tail probability of the arc-length statistic (C back-end)	al_pvalue
Scale by arc-length band matching, in the scale-equivariant standardised form (C back-end)	al_scale
The uncorrected band-matching scale estimator (C back-end)	al_scale_raw
Arc-length goodness-of-fit statistic (C back-end)	al_statistic
Arc-length goodness-of-fit test	al_test
Arc-length generator: transform a bounded-support base into a new distribution	arc_generator dgen pgen rgen
Largest admissible shape parameter of the smooth circular family	arcc_c3max
Exact confidence interval for the shape parameter of the wrapped order-three family	arcc_exact_ci
Goodness of fit of a fitted circular arc-length member	arcc_gof
The smooth circular arc-length family	arccirc darccirc qd_arccirc Q_arccirc rarccirc rho_arccirc trigmom_arccirc
Fejer-Riesz form of the circular arc-length family	arccirc_fr darccirc_fr qd_arccirc_fr Q_arccirc_fr rarccirc_fr trigmom_arccirc_fr
Construct a quantile arc-length distribution	arclength arcq darcq parcq qarcq rarcq
Bayesian arc-length goodness-of-fit evidence	bb_evidence
Bayesian-bootstrap posterior arc-length discrepancies	bb_post_disc
Null reference distribution of the arc-length discrepancy	bb_ref_disc
Beta-companion distribution function	bc_cdf
Beta-companion density	bc_pdf
Beta-companion quantile function (standardised support)	bc_q
Arc length of the empirical characteristic function (C back-end)	cf_arclength
Closed-form characteristic-function arc length for named families	cf_arclength_family
Arc-length tempering of a von Mises base	dtemper_vm trigmom_temper_vm
Equivalence curve	eq_bstar
Closed-form equivalence discrepancy	eq_E
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))	eq_readings eq_readings_vsl
Quadratic shoulder and mode of the kernel family	eq_ub_quad
The equivalence-system paper's fitting and simulation loops, in the back end	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
Method-of-moments fit of the smooth circular arc-length family	fit_arccirc
Closed-form fit of the Fejer-Riesz circular arc-length family	fit_arccirc_fr
Fit an arcq distribution to data by matching L-moments	fit_arcq
Closed-form L-moment fit of the order-two arcq family	fit_arcq_cf
Band arc lengths of a scaled kappa curve and of a data polyline	k4_band_model k4_band_sample
Exact mean of the tropical band arc length under Gaussian error	k4_band_trop_mean
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)	k4_fit_aleq k4_fit_lmom k4_fit_nalr k4_fit_nls
Variable-projection fit of the drifted kappa response	k4_fit_varpro
One-way variance components and the intraclass correlation	k4_icc
Distance from fitted shapes to the equivalence locus	k4_locus_dist
The fitting-method multiverse of one induction run: eight admissible pipelines under one moving-block residual bootstrap	k4_mv_boot
Four-parameter kappa quantile, distribution and density functions	k4_cdf k4_pdf k4_q
The two standard induction-period readings of a fitted kappa curve	k4_readings
Running median with shrinking symmetric windows at the edges	k4_runmed
Theoretical L-moment ratios of the standard kappa distribution	k4_tau34
Circular L-moments	admiss_rho factorise_rho lmom_circ qmin_rho rho_from_lmom
Theoretical L-moments of an arcq distribution	lmoments
L-moment ratios (tau_3, tau_4, ...) from a vector of L-moments	lmratios
Sample L-moments of data	sample_lmoments

Package: arcstat 0.3.1

arcstat: Arc-Length Statistics: Goodness of Fit, Distributions and a Bayesian Test

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