R Core Team — R statistical computing
R Core Team (2026). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna.
Supports: core scalar D/P/Q/R conventions and the audited src/nmath lineage.
Scientific provenance
Find the method behind the feature
Search by method, class, author, topic, or DOI. Entries point to the primary paper or canonical numerical reference; implementation lineage is recorded separately when JDistlib follows R or another audited codebase.
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Probability & numerical distributions
Distributions, simulation, and numerical construction
JDistlib contributed-distribution provenance ledger
JDistlib maintainers. Contributed Distribution Provenance. Versioned reference implementations, licenses, parameterizations, and independent verification for non-R distribution families.
Supports: every contributed scalar, multivariate, matrix, and compound-count class in the distribution catalog. Where a distinct scientific or numerical method governs an implementation, its primary paper appears as a separate entry on this page.
Matsumoto & Nishimura (1998) — Mersenne Twister
Matsumoto, M., & Nishimura, T. (1998). “Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator.” ACM TOMACS 8(1), 3–30.
Supports: MersenneTwister and explicit seeded simulation examples.
Genz (1992) — multivariate normal probabilities
Genz, A. (1992). “Numerical Computation of Multivariate Normal Probabilities.” Journal of Computational and Graphical Statistics 1(2), 141–149.
Supports: randomized conditional integration for multivariate normal, Student-t, Cauchy, and log-normal rectangle probabilities.
Benton & Krishnamoorthy (2003) — noncentral mixtures
Benton, D., & Krishnamoorthy, K. (2003). “Computing Discrete Mixtures of Continuous Distributions: Noncentral Chi-square, Noncentral t and the Distribution of the Square of the Sample Multiple Correlation Coefficient.” Computational Statistics & Data Analysis 43, 249–267.
Supports: centered Poisson-mixture evaluation used by noncentral probability laws and their accuracy audit.
Birnbaum & Saunders (1969) — fatigue-life distribution
Birnbaum, Z. W., & Saunders, S. C. (1969). “A New Family of Life Distributions.” Journal of Applied Probability 6(2), 319–327.
Supports: BirnbaumSaunders / fatigue-life distribution.
Jørgensen (1987) — exponential dispersion models
Jørgensen, B. (1987). “Exponential Dispersion Models.” Journal of the Royal Statistical Society B 49(2), 127–162.
Supports: Tweedie exponential-dispersion parameterization and compound Poisson–gamma interpretation.
Piessens et al. (1983) — QUADPACK
Piessens, R., de Doncker-Kapenga, E., Überhuber, C. W., & Kahaner, D. K. (1983). QUADPACK: A Subroutine Package for Automatic Integration. Springer.
Supports: adaptive finite, semi-infinite, and whole-line quadrature used by numerical distributions and integration APIs.
Brent (1973) — derivative-free root finding
Brent, R. P. (1973). Algorithms for Minimization without Derivatives. Prentice-Hall.
Supports: bracketed scalar root finding, numerical quantile inversion, and one-dimensional optimization.
Gilks & Wild (1992) — adaptive rejection sampling
Gilks, W. R., & Wild, P. (1992). “Adaptive Rejection Sampling for Gibbs Sampling.” Applied Statistics 41(2), 337–348.
Supports: log-concave adaptive-rejection sampling and related custom-law sampling strategy.
Anderson & Darling (1952) — weighted EDF tests
Anderson, T. W., & Darling, D. A. (1952). “Asymptotic Theory of Certain Goodness of Fit Criteria Based on Stochastic Processes.” Annals of Mathematical Statistics 23(2), 193–212.
Supports: Anderson–Darling and the weighted empirical-distribution-function test family.
Efron (1979) — bootstrap
Efron, B. (1979). “Bootstrap Methods: Another Look at the Jackknife.” Annals of Statistics 7(1), 1–26.
Supports: resampling-based p-values, uncertainty intervals, and fitted-model refitting guidance.
Hypothesis testing & multiplicity
Family-wise error, FDR, online testing, and q-values
Holm (1979) — sequentially rejective Bonferroni
Holm, S. (1979). “A Simple Sequentially Rejective Multiple Test Procedure.” Scandinavian Journal of Statistics 6(2), 65–70.
Supports: Holm step-down FWER adjustment and weighted Holm lineage.
Hochberg (1988) and Hommel (1988) — step-up FWER procedures
Hochberg, Y. (1988). “A Sharper Bonferroni Procedure for Multiple Tests of Significance.” Biometrika 75(4), 800–802. Hommel, G. (1988). “A Stagewise Rejective Multiple Test Procedure Based on a Modified Bonferroni Test.” Biometrika 75(2), 383–386.
Supports: Hochberg and Hommel adjustments.
Benjamini & Hochberg (1995) — false discovery rate
Benjamini, Y., & Hochberg, Y. (1995). “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing.” JRSS B 57(1), 289–300.
Supports: BH adjusted p-values, thresholds, rejections, and weighted extensions.
Benjamini & Yekutieli (2001) — FDR under dependence
Benjamini, Y., & Yekutieli, D. (2001). “The Control of the False Discovery Rate in Multiple Testing under Dependency.” Annals of Statistics 29(4), 1165–1188.
Supports: BY adjustment under arbitrary dependence.
Benjamini, Krieger & Yekutieli (2006) — adaptive two-stage FDR
Benjamini, Y., Krieger, A. M., & Yekutieli, D. (2006). “Adaptive Linear Step-up Procedures that Control the False Discovery Rate.” Biometrika 93(3), 491–507.
Supports: two-stage BKY decisions and estimated-null count.
Storey (2002) — q-values and null proportion
Storey, J. D. (2002). “A Direct Approach to False Discovery Rates.” JRSS B 64(3), 479–498.
Supports: q-values and estimation of the true-null proportion π₀.
Benjamini & Hochberg (1997) — weighted multiple testing
Benjamini, Y., & Hochberg, Y. (1997). “Multiple Hypotheses Testing with Weights.” Scandinavian Journal of Statistics 24(3), 407–418.
Supports: prespecified weighted BH/Bonferroni procedures.
Gavrilov, Benjamini & Sarkar (2009) — adaptive step-down FDR
Gavrilov, Y., Benjamini, Y., & Sarkar, S. K. (2009). “An Adaptive Step-down Procedure with Proven FDR Control under Independence.” Annals of Statistics 37(2), 619–629.
Supports: GBS adaptive step-down decisions.
Benjamini & Bogomolov (2014) — selective grouped testing
Benjamini, Y., & Bogomolov, M. (2014). “Selective Inference on Multiple Families of Hypotheses.” JRSS B 76(1), 297–318.
Supports: two-level grouped BH with selective average-FDR control.
Ramdas et al. (2017, 2018) — LORD++ and SAFFRON
Ramdas, A. et al. (2017). “Online Control of the False Discovery Rate with Decaying Memory.” NeurIPS. Ramdas, A. et al. (2018). “SAFFRON: An Adaptive Algorithm for Online Control of the False Discovery Rate.” AISTATS/PMLR 80.
Supports: stateful LORD++ and SAFFRON controllers for ordered hypothesis streams.
Döhler, Durand & Roquain (2018) — discrete FDR
Döhler, S., Durand, G., & Roquain, E. (2018). “New FDR Bounds for Discrete and Heterogeneous Tests.” Electronic Journal of Statistics 12, 1867–1900.
Supports: DBH step-up/down procedures using attainable p-values and null CDFs.
Dependence modeling
Copulas, mixed margins, selection, and vines
Sklar (1959) — copula decomposition
Sklar, A. (1959). “Fonctions de répartition à n dimensions et leurs marges.” Publications de l’Institut de Statistique de l’Université de Paris 8, 229–231.
Supports: separation of marginal laws from copula dependence in continuous and mixed joint models.
Clayton (1978) — Clayton copula
Clayton, D. G. (1978). “A Model for Association in Bivariate Life Tables and Its Application in Epidemiological Studies of Familial Tendency in Chronic Disease Incidence.” Biometrika 65(1), 141–151.
Supports: ClaytonCopula and its lower-tail dependence interpretation.
Gumbel (1960) — Gumbel dependence family
Gumbel, E. J. (1960). “Bivariate Exponential Distributions.” Journal of the American Statistical Association 55(292), 698–707.
Supports: GumbelCopula / Gumbel–Hougaard upper-tail dependence.
Aas et al. (2009) — pair-copula constructions
Aas, K., Czado, C., Frigessi, A., & Bakken, H. (2009). “Pair-copula Constructions of Multiple Dependence.” Insurance: Mathematics and Economics 44(2), 182–198.
Supports: C-vines, D-vines, sequential pair-copula fitting, and conditional simulation.
Schwarz (1978) — Bayesian information criterion
Schwarz, G. (1978). “Estimating the Dimension of a Model.” Annals of Statistics 6(2), 461–464.
Supports: BIC-based copula and parametric model selection.
Bayesian computation
Samplers, diagnostics, predictive assessment, and model spaces
Metropolis et al. (1953) and Hastings (1970) — MCMC acceptance
Metropolis, N. et al. (1953). “Equation of State Calculations by Fast Computing Machines.” Journal of Chemical Physics 21, 1087–1092. Hastings, W. K. (1970). “Monte Carlo Sampling Methods Using Markov Chains and Their Applications.” Biometrika 57(1), 97–109.
Supports: random-walk Metropolis, asymmetric proposal correction, and Metropolis-within-Gibbs kernels.
Duane et al. (1987) and Hoffman & Gelman (2014) — HMC and NUTS
Duane, S. et al. (1987). “Hybrid Monte Carlo.” Physics Letters B 195(2), 216–222. Hoffman, M. D., & Gelman, A. (2014). “The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo.” JMLR 15, 1593–1623.
Supports: HMC, NoUTurnSampler, leapfrog integration, U-turn termination, and dual-averaging step-size adaptation.
Neal (2003) — slice sampling
Neal, R. M. (2003). “Slice Sampling.” Annals of Statistics 31(3), 705–767.
Supports: scalar slice sampling and stepping-out/shrinkage updates.
Vehtari et al. (2021) — rank-normalized R-hat and ESS
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P.-C. (2021). “Rank-normalization, Folding, and Localization: An Improved R-hat for Assessing Convergence of MCMC.” Bayesian Analysis 16(2), 667–718.
Supports: split/folded rank R-hat, bulk and tail ESS, MCSE, and rank plots.
Betancourt (2017) — HMC geometry and diagnostics
Betancourt, M. (2017). “A Conceptual Introduction to Hamiltonian Monte Carlo.” arXiv:1701.02434.
Supports: geometric interpretation of divergences, tree depth, energy behavior, E-BFMI, and funnel diagnostics.
Papaspiliopoulos, Roberts & Sköld (2007) — centered/non-centered parameterizations
Papaspiliopoulos, O., Roberts, G. O., & Sköld, M. (2007). “A General Framework for the Parametrization of Hierarchical Models.” Statistical Science 22(1), 59–73.
Supports: non-centered hierarchical parameterization and funnel remediation.
Green (1995) — reversible-jump MCMC
Green, P. J. (1995). “Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination.” Biometrika 82(4), 711–732.
Supports: variable-dimensional states, dimension matching, Jacobians, model-selection probabilities, and add/drop/swap moves.
Zhang et al. (2022) — Pathfinder
Zhang, L. et al. (2022). “Pathfinder: Parallel Quasi-Newton Variational Inference.” JMLR 23(306), 1–49.
Supports: multi-path quasi-Newton posterior approximation and MCMC initialization.
Vehtari, Gelman & Gabry (2017) — PSIS-LOO
Vehtari, A., Gelman, A., & Gabry, J. (2017). “Practical Bayesian Model Evaluation Using Leave-one-out Cross-validation and WAIC.” Statistics and Computing 27, 1413–1432.
Supports: Pareto-smoothed importance-sampling LOO, Pareto-k diagnostics, and model comparison.
Watanabe (2010) — WAIC
Watanabe, S. (2010). “Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory.” Journal of Machine Learning Research 11, 3571–3594.
Supports: WAIC from pointwise log-likelihood draws.
Yao et al. (2018) — Bayesian predictive stacking
Yao, Y., Vehtari, A., Simpson, D., & Gelman, A. (2018). “Using Stacking to Average Bayesian Predictive Distributions.” Bayesian Analysis 13(3), 917–1007.
Supports: predictive stacking weights and model averaging.
Modern HMC adaptation — ChEES, SNAPER, nested R-hat, and adjusted MCLMC
Hoffman et al. (2021), “An Adaptive-MCMC Scheme for Setting Trajectory Lengths in Hamiltonian Monte Carlo”; Sountsov & Hoffman (2021), “Focusing on Difficult Directions for Learning HMC Trajectory Lengths”; Margossian et al. (2024), nested R-hat; Robnik et al. (2025), adjusted microcanonical HMC.
Supports: ChEES/SNAPER static HMC, many-short-chain diagnostics, and adjusted MCLMC workflows.
Financial probability
Risk, option-implied laws, transforms, and extremes
Black & Scholes (1973) — European option pricing
Black, F., & Scholes, M. (1973). “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy 81(3), 637–654.
Supports: checked Black–Scholes prices and implied-volatility inversion.
Breeden & Litzenberger (1978) — option-implied distributions
Breeden, D. T., & Litzenberger, R. H. (1978). “Prices of State-Contingent Claims Implicit in Option Prices.” Journal of Business 51(4), 621–651.
Supports: extraction of smooth risk-neutral densities and CDFs from arbitrage-consistent option curves.
Carr & Madan (1999) — FFT option valuation
Carr, P., & Madan, D. B. (1999). “Option Valuation Using the Fast Fourier Transform.” Journal of Computational Finance 2(4), 61–73.
Supports: characteristic-function Fourier inversion and option-transform calculations.
Rockafellar & Uryasev (2000) — conditional value-at-risk
Rockafellar, R. T., & Uryasev, S. (2000). “Optimization of Conditional Value-at-Risk.” Journal of Risk 2(3), 21–41.
Supports: expected shortfall / CVaR functionals and loss-tail optimization interpretation.
Newey & Powell (1987) — expectiles
Newey, W. K., & Powell, J. L. (1987). “Asymmetric Least Squares Estimation and Testing.” Econometrica 55(4), 819–847.
Supports: expectile risk measures and asymmetric squared-loss interpretation.
Balkema & de Haan (1974) and Pickands (1975) — peaks over threshold
Balkema, A. A., & de Haan, L. (1974). “Residual Life Time at Great Age.” Annals of Probability 2(5), 792–804. Pickands, J. (1975). “Statistical Inference Using Extreme Order Statistics.” Annals of Statistics 3(1), 119–131.
Supports: GPD threshold excesses, tail-index/return-level estimation, and EVT diagnostics.
Madan & Seneta (1990) and Carr et al. (2002) — Lévy return models
Madan, D. B., & Seneta, E. (1990). “The Variance Gamma Model for Share Market Returns.” Journal of Business 63(4), 511–524. Carr, P., Geman, H., Madan, D. B., & Yor, M. (2002). “The Fine Structure of Asset Returns.” Journal of Business 75(2), 305–332.
Supports: variance-gamma and CGMY/tempered-stable characteristic functions and increment laws.
Scientific computing
Differential equations, autodiff, and linear algebra
Dormand & Prince (1980) — embedded RK5(4)
Dormand, J. R., & Prince, P. J. (1980). “A Family of Embedded Runge-Kutta Formulae.” Journal of Computational and Applied Mathematics 6(1), 19–26.
Supports: adaptive explicit RK45 integration for non-stiff ODEs and sensitivities.
Hindmarsh et al. (2005) — SUNDIALS solver architecture
Hindmarsh, A. C. et al. (2005). “SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers.” ACM TOMS 31(3), 363–396.
Supports: stiff BDF, nonlinear algebraic, DAE, sensitivity, and Newton-style solver design.
Baydin et al. (2018) — automatic differentiation
Baydin, A. G., Pearlmutter, B. A., Radul, A. A., & Siskind, J. M. (2018). “Automatic Differentiation in Machine Learning: A Survey.” JMLR 18(153), 1–43.
Supports: reverse-mode differentiation, reusable tapes, and atomic differentiable kernels.
Carpenter et al. (2017) — Stan probabilistic programming
Carpenter, B. et al. (2017). “Stan: A Probabilistic Programming Language.” Journal of Statistical Software 76(1), 1–32.
Supports: Stan language semantics used as the compatibility target for supported ordinary .stan source.
Anderson et al. (1999) — LAPACK
Anderson, E. et al. (1999). LAPACK Users’ Guide, 3rd ed. SIAM.
Supports: dense BLAS/LAPACK semantics for LU, Cholesky, QR, eigen, and SVD operations across providers.
Chen et al. (2008) — CHOLMOD sparse Cholesky
Chen, Y., Davis, T. A., Hager, W. W., & Rajamanickam, S. (2008). “Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate.” ACM TOMS 35(3), Article 22.
Supports: supernodal sparse Cholesky factorization and optional native CHOLMOD acceleration.
Coverage and corrections
Keep provenance auditable
This catalog groups closely related API variants under the paper that introduced or established the method. Distribution implementation sources and versioned verification live in the provenance ledger. If a citation or method mapping is incomplete, please open a GitHub issue with the class, method, and proposed primary source.