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Third-party code and algorithmic references

Plöttr's own code is MIT (see LICENSE). This file lists everything else — vendored third-party code, ports of public-domain implementations, and the algorithmic references behind the statistical computations. Each entry names what's used, where it's used, and the licensing posture.

The intent is one-stop transparency: a peer reviewer should be able to read this page and verify that nothing in the repo is an unattributed copy of licensed code. Inline citations exist throughout the statistics kernel (tools/_core/stats/) and the shared helpers under tools/_core/ — this file consolidates them. The complete, DOI-verified research bibliography behind Plöttr's methods is the References section of the README; this file focuses on code provenance and licensing.

Vendored binaries

Component Path License Notes
React 18 vendor/react.production.min.js MIT (Meta) Unmodified production bundle. @license header retained inline. Standalone MIT text in vendor/LICENSE-react.txt.
ReactDOM 18 vendor/react-dom.production.min.js MIT (Meta) Same as above.

Both are vendored so a cloned copy works without network access — Plöttr is designed to run from any static host (or directly off the filesystem) with no runtime CDN dependency.

Ports with public-domain provenance

Component Where Source Provenance
betacf (continued fraction for the regularized incomplete beta) tools/_core/stats/dist.ts Cephes Mathematical Library, incbet.c (incbcf form), Stephen L. Moshier, "Cephes Math Library Release 2.8" (2000), https://www.netlib.org/cephes/ Public domain (author dedication).
gammainc (regularized lower incomplete gamma — series form) tools/_core/stats/dist.ts Cephes Mathematical Library, igam.c Public domain (author dedication).
gammainc_upper (regularized upper incomplete gamma — continued fraction) tools/_core/stats/dist.ts Cephes Mathematical Library, igam.c (igamc form) Public domain (author dedication).
seededRandom (Park-Miller minimal-standard LCG) tools/_core/numeric.ts S. K. Park & K. W. Miller, "Random number generators: Good ones are hard to find" (CACM, 1988); algorithm originated with D. H. Lehmer, 1951. Public-domain algorithm; constants 16807 / 2147483647 are the algorithm.
gammaln Lanczos coefficients (g = 7) tools/_core/stats/dist.ts Paul Godfrey, "A note on the computation of the convergent Lanczos complex Gamma approximation" (2001) Coefficients are public-domain in spirit; widely circulated as the standard g = 7 reference table.

The Cephes ports use a three-term recurrence (pkm/qkm with periodic big/biginv rescaling). Plöttr-specific polish — log-space final exponentiation in gammainc / gammainc_upper, and a √a-scaled iteration cap so chi2cdf and ptukey stay accurate at huge df — is layered on top of the Cephes recurrence. Constants (CEPHES_BIG = 2^52, CEPHES_BIGINV = 2^-52, CEPHES_MACHEP = 1.11e-16) match Cephes' incbet.c / igam.c literally. See tools/_core/stats/dist.ts lines ~170–340 for the attribution block (header comment plus the betacf / gammainc / gammainc_upper bodies).

Algorithmic references (algorithm-only — no code copied)

These are textbook statistical algorithms with attribution to their publication. Algorithms themselves are not copyrightable; we cite to give a reviewer or downstream user a path to the canonical description without having to reverse-engineer the implementation. All implementations below are independently coded.

Distribution functions

  • normcdf / normsf — Abramowitz & Stegun, Handbook of Mathematical Functions, §26.2.17 (1964). U.S. government publication; public domain. Coefficients (0.2316419, 0.31938153, −0.356563782, …) are the standard A&S table.
  • norminv — Peter J. Acklam, "An algorithm for computing the inverse normal cumulative distribution function" (2003). Acklam explicitly waived restrictions ("freely usable for any purpose").
  • Studentized-range distribution (ptukey, qtukey, _wprob_upper) — independently derived 48-node Gauss-Legendre quadrature on y = log(s), with bracketing from chi2inv(1e-10, df) / chi2inv(1−1e-10, df). Does not derive from R's GPL ptukey.c (which uses Gauss-Hermite tables from AS 190, Copenhaver & Holland 1988); the algebraic factorisation a^(k−1) − b^(k−1) = (a−b)·Σ a^(k−2−j)·b^j for the upper tail is documented in the source comments at tools/_core/stats/posthoc.ts ~line 35.
  • Noncentral t / F / χ² (nctcdf, ncf_sf, ncchi2cdf) — textbook Poisson-mixture and chi²-mixture forms, mode-centred enumeration. The closed-form normal-approximation short-circuit (if halfLam > 500 && d2 > 4) for ncf_sf is Plöttr-specific polish.
  • gammaln — Lanczos (1964) approximation with g = 7 coefficients (Godfrey 2001 reference table). The decimal expansions are widely circulated.

Statistical tests

  • Shapiro–Wilk normality test — Royston, "A remark on Algorithm AS 181: the W test for normality" (Applied Statistics 44(4), 1995), with AS R94 polynomial approximations for the tail. Implementation re-derives the Royston coefficients analytically; the AS R94 Fortran (StatLib, "may be used freely for non-commercial purposes") is not the source. Expected values of normal order statistics use Blom's approximation (Blom 1958).
  • Mann–Whitney U — tie correction follows E. L. Lehmann, Nonparametrics (1975).
  • Kruskal–Wallis — tie correction follows S. Siegel & N. J. Castellan, Nonparametric Statistics for the Behavioral Sciences (2nd ed., 1988). Effect-size formulas (η², ε²) follow Tomczak & Tomczak, "The need to report effect size estimates revisited" (2014).
  • Tukey HSD — studentized-range survival via the in-house ptukey_upper (see Distribution functions above).
  • Games–Howell — formulas from Day & Quinn, "Comparisons of treatments after an analysis of variance in ecology" (Ecological Monographs 59(4), 1989).
  • Dunn's test (Bonferroni / BH-adjusted) — original formula from O. J. Dunn, "Multiple comparisons using rank sums" (Technometrics 6(3), 1964); tie correction following Siegel & Castellan (above).
  • Benjamini–Hochberg FDR control — Benjamini & Hochberg, "Controlling the false discovery rate" (JRSS-B 57(1), 1995). Trivial 8-line implementation.
  • Compact letter display — Piepho, "An algorithm for a letter-based representation of all-pairwise comparisons" (Journal of Computational and Graphical Statistics 13(2), 2004).
  • Rank-biserial correlation — D. Kerby, "The simple difference formula: An approach to teaching nonparametric correlation" (Comprehensive Psychology 3(1), 2014).
  • Cohen's d / Hedges' g — standard formulas from J. Cohen, Statistical Power Analysis (2nd ed., 1988); Hedges' bias-correction factor from L. V. Hedges, "Distribution theory for Glass's estimator of effect size" (Journal of Educational Statistics 6(2), 1981).

Set-theoretic and combinatorial

  • Multi-set intersection enrichment / depletion — M. Wang, Y. Zhao & B. Zhang, "Efficient test and visualization of multi-set intersections" (Scientific Reports 5, article 16923, 2015), https://doi.org/10.1038/srep16923 — the algorithmic basis for the SuperExactTest R package. Implementation is independently derived from the iterated-hypergeometric description; no R code is copied.

Graphics / chart helpers

  • Kernel density estimate — Gaussian kernel + Silverman's rule-of-thumb bandwidth (B. W. Silverman, Density Estimation for Statistics and Data Analysis, 1986). Independent implementation; does not derive from scipy's gaussian_kde or d3's bin.
  • makeTicks / makeLogTicks "nice numbers" tick rounding — Heckbert, "Nice numbers for graph labels", Graphics Gems I (Academic Press, 1990). Algorithm only — implementation does not derive from d3-scale's ticks().
  • Hierarchical clustering (hclust) — naive O(n³) Lance–Williams update (Lance & Williams, "A general theory of classificatory sorting strategies", Computer Journal 9(4), 1967) with UPGMA / single / complete linkages. Does not derive from scipy's _hierarchy.pyx (NN-chain compression) or ml-hclust (priority-queue NN-chain).
  • k-means / k-means++ — Lloyd 1982 / Arthur & Vassilvitskii, "k-means++: the advantages of careful seeding" (SODA, 2007). Algorithm only.

Color and palettes

  • Okabe–Ito qualitative palette — Wong, "Color blindness", Nature Methods 8 (2011). The eight-colour set was designed for accessibility to colour-vision-deficient readers and is widely shared in the scientific community; we use it as the default qualitative palette throughout Plöttr.
  • Sequential and diverging palettes — viridis / plasma / magma / inferno derived from the Matplotlib palettes (released CC0 / public domain by their authors Stéfan van der Walt & Nathaniel Smith); cividis from Nuñez, Anderton & Renslow, "Optimizing colormaps with consideration for color vision deficiency to enable accurate interpretation of scientific data" (PLOS ONE 13(7), e0199239, 2018), https://doi.org/10.1371/journal.pone.0199239.
  • ColorBrewer qualitative palettes (set1 / set2 / set3 / dark2 / paired / pastel1 / pastel2) — © Cynthia Brewer, Mark Harrower and The Pennsylvania State University; licensed under the Apache License 2.0. Used as discrete-palette presets in tools/_shell/discrete-palette.ts.
  • Tableau10 qualitative palette — the ten-colour categorical set originated with Tableau Software and is widely reproduced across visualisation tools; used as a discrete-palette preset in tools/_shell/discrete-palette.ts. Plöttr asserts no licence over it.

CSV parsing

  • tokenizeDelimited, parseRaw — hand-written RFC 4180 state machine. Independent implementation; does not derive from csv-parse, papaparse, or any other open-source CSV library.

Datasets

Built-in R datasets (iris, PlantGrowth, ToothGrowth, mtcars, etc.) are referenced by the benchmark suite at benchmark/run-r.R for cross-validation. The benchmark loads them from R at runtime — values are not redistributed in this repository. The values themselves are facts (e.g. iris is Anderson 1935 / Fisher 1936) and not copyrightable.

The single bundled dataset is the classic 150-row iris flower measurements, inlined verbatim in tools/scatter/app.tsx — public domain (Anderson 1935; Fisher 1936). The inline comment there cites both papers.