Changelog

Source: NEWS.md

gkwdist 1.1.5

Critical Bug Fixes

• dgkw() returned zero for every input (gkw.cpp, utils.h): the package’s numerical helpers log1mexp() and log1pexp() collide with functions of the same name in R’s public Rmath.h API, which use the opposite convention (log(1 - exp(-x)) for x >= 0). In translation units where Rmath.h’s macro was active, calls bound to R’s version, which returns NaN for the negative arguments used here; every density evaluation then failed its finiteness guard and returned 0. The helpers are now named gkw_log1mexp() and gkw_log1pexp(). The sub-family densities were unaffected, as was llgkw(), which routes through vec_log1mexp().

• Log-likelihoods of EKw, KKw and BKw were wrong for data near zero (ekw.cpp, kkw.cpp, bkw.cpp): these routines clamped v = 1 - x^alpha and w = 1 - v^beta at 1e-10 instead of working in log space. For small x and moderate alpha, x^alpha rounds to 1 in double precision and w collapses to zero, so the clamp replaced log(w) = -53 by log(1e-10) = -23. Deviations reached 6,100 log-units, which silently corrupts AIC, BIC and likelihood ratio tests. All three families now use the same gkw_log1mexp() formulation as gkw.cpp, and their scores and Hessians are expressed as ratios of logarithms.

• Mixed second derivatives were zeroed at degenerate parameter values (bkw.cpp, ekw.cpp, kkw.cpp): guards of the form if (abs(p - 1) > eps) gated mixed partial derivatives that do not carry the vanishing factor. Because d2l/dalpha dgamma is obtained by differentiating (gamma-1)*log(w) once in gamma, the (gamma-1) factor is consumed and the term survives at gamma = 1. hsbkw() returned 0 where the correct value was 271.12; hsekw() and hskkw() had the same defect at beta = 1.

• grkkw() clamped gradient terms at 1000 (kkw.cpp): arbitrary std::min(..., 1000.0) caps distorted the score in beta by up to 5%. The same clamp appeared as effective_delta inside llkkw(), capping the likelihood for delta > 1000. This is the defect removed from ekw.cpp in 1.1.3, which had survived here.

• grkkw() and hskkw() skipped the z block at delta = 0 (kkw.cpp): the shortcut omitted sum(log(z)) from dl/ddelta and zeroed d2l/dalpha ddelta, d2l/dbeta ddelta and d2l/ddelta dlambda, none of which carry a delta factor. delta = 0 is a valid interior value of the likelihood.

• The Beta sub-family rejected delta = 0 (utils.h): check_beta_pars() required delta > 0, unlike the other five validators. Since the sub-family is parameterised as Beta(gamma, delta + 1), delta = 0 is the legitimate Beta(gamma, 1) boundary; dbeta_(), pbeta_(), qbeta_(), rbeta_(), llbeta(), grbeta() and hsbeta() all returned NA/Inf there.

Validation

• test-boundary-derivatives.R (new): every gradient component and every Hessian entry of all seven sub-families is now compared individually against two independent references, the general GKw routines restricted to the constrained parameter point and numDeriv Richardson extrapolation, over grids that include the degenerate values gamma = 1, beta = 1, lambda = 1 and delta = 0 and samples containing observations near zero.

• test-density-correctness.R (new): densities are checked to integrate to one, to agree with the general GKw density at the constrained parameter point, to match base R for the Beta and closed-form Kumaraswamy cases, and to be the derivative of the corresponding distribution function. The previous PDF tests asserted only type, length, non-negativity and finiteness, all of which a vector of zeros satisfies.

Accuracy after the fixes

Componentwise maximum relative error over 720 parameter configurations per family, against the general GKw routines and against numDeriv:

Family	log-likelihood	gradient	Hessian
GKw	1.5e-11	1.5e-08	1.5e-07
BKw	1.6e-12	3.7e-08	3.6e-08
KKw	3.1e-13	3.5e-08	4.9e-08
EKw	5.4e-14	7.8e-09	2.7e-08
Mc	3.5e-13	2.5e-09	9.5e-10
Kw	4.1e-15	7.2e-10	1.2e-09
Beta	7.2e-15	4.6e-10	8.9e-11

The residual gradient and Hessian errors are at the accuracy limit of Richardson extrapolation itself; against the GKw reference all seven families agree to 1e-13.

Documentation and Project Infrastructure

• inst/paper/: the JOSS manuscript was rewritten. It now positions the package explicitly as the distribution layer of the GKw ecosystem, records that the split from gkwreg was made at the request of JOSS reviewers during that package’s review, reports the measured validation and timing results in place of the previous unverified figures, and follows the current JOSS AI disclosure policy. The bibliography was expanded to 19 entries with DOIs verified against Crossref.

• CONTRIBUTING.md and CODE_OF_CONDUCT.md (new): contribution workflow, support expectations, governance, and the testing standard numerical contributions are held to. The contributing guide documents the cross-check that makes bug reports actionable: every sub-family routine must agree with the general GKw routine evaluated at the corresponding constrained parameter point.

• README: the claim that the C++ routines are “10-50x faster than equivalent R implementations” was replaced with measured figures. The original benchmark compared -sum(log(dkw(x, 2, 3))) against llkw(), which is C++ against C++ plus R loop overhead, and gives roughly 3x. The genuine gain is in the derivatives: the analytical score is about 9x faster than Richardson extrapolation and the analytical Hessian about 38x faster at n = 20,000.

• inst/CITATION: updated to version 1.1.5 and pointed at the CRAN canonical URL; it had been stale at version 1.0.8.

• Test coverage rose from 70.8% to 74.2% of combined R and C++ lines. The largest single gain is in src/gkw.cpp (42.9% to 71.5%), which reflects that dgkw() now executes its density computation instead of falling through to its finiteness guard.

gkwdist 1.1.4

CRAN release: 2026-05-28

CRAN Fix

• test-mle-performance.R: Added skip_on_cran() to all timing-based benchmark tests. These tests compare wall-clock times of analytical vs. numerical gradients and are inherently unreliable on shared/loaded CRAN check machines, causing spurious ERROR results. The tests remain available for local development.

gkwdist 1.1.3

CRAN release: 2026-05-21

Bug Fixes

• llgkw() invalid parameter return (gkw.cpp): Fixed critical error where the negative log-likelihood returned R_NegInf (−∞) for invalid parameters instead of R_PosInf (+∞). Gradient-based MLE optimizers interpret −∞ as a global minimum, causing them to converge to the invalid boundary rather than the true MLE.

• gkwinit.cpp — delta validation (gkwinit.cpp): Fixed internal gkw_pdf() rejecting delta = 0 (a valid GKw parameter value) due to a strict delta <= 0 check that should have been delta < 0.

• gkwinit.cpp — EKw/Kw sub-family PDF mapping (gkwinit.cpp): Fixed ekw_pdf() and kw_pdf() passing delta = 1 instead of the correct delta = 0 when delegating to gkw_pdf(). EKw and Kw are GKw sub-families with delta = 0, not delta = 1. This produced wrong starting values for MLE of these families.

• hsbkw() — v^(β−1) computation (bkw.cpp): Fixed the Hessian of the BKw negative log-likelihood returning a wrong value for β < 1. The ternary expression (beta > 1.0) ? v_beta/v : 1.0 coincidentally produces the correct result for β = 1 but is wrong for all 0 < β < 1. Replaced with the exact formula safe_exp((beta - 1.0) * ln_v).

Numerical Stability

• safe_exp() underflow scaling (utils.h): Fixed a systematic 10× error in the moderate-underflow branch. The previous implementation used DBL_MIN_SAFE * exp(x − log(DBL_MIN)) where DBL_MIN_SAFE = 10 * DBL_MIN, yielding 10 * exp(x) instead of exp(x). The fix uses DBL_MIN * exp(x − log(DBL_MIN)) = exp(x) exactly.

• dgkw() silent boundary truncation removed (gkw.cpp): Removed a block that silently skipped data points within SQRT_EPSILON^(1/α) of 0 or 1, returning density 0 for those points without warning. The log-space computation handles near-boundary values correctly without this truncation.

• llekw() / grekw() — lambda clamping removed (ekw.cpp): Removed the arbitrary cap lambda_factor = min(lambda_factor, 1000) applied to gradient and Hessian terms when λ > 1000. This distorted optimization for large-λ scenarios and produced incorrect standard errors.

Code Quality

• gkwinit.cpp: Removed using namespace Rcpp; at file scope; replaced with explicit Rcpp:: qualifications. Added NA/NaN filtering before moment computation to prevent silent corruption when input data contains missing values.

• bkw.cpp: Removed spurious try/catch blocks wrapping Rcpp::as<arma::vec>() conversions in grbkw() and hsbkw(). These conversions cannot throw in this context and the silent fallback masked type errors.

• gkw.cpp / ekw.cpp: Refactored Hessian accumulation to build only the upper triangle inside the observation loop and symmetrize once afterwards with arma::symmatu(), eliminating O(n × p²) redundant assignments.

• utils.h — vec_safe_pow() UB guard: Added guard preventing undefined behaviour when casting large y_rounded values (> INT_MAX) to int for odd-exponent sign detection.

• utils.h — vec_safe_pow() SIMD fast path: Added an early-return path arma::exp(y * arma::log(x)) for the common case (y > 0, all x > 0) that is fully auto-vectorizable, improving throughput in gradient/Hessian evaluation.

gkwdist 1.1.2

CRAN release: 2026-01-08

Code Cleanup and Testing Enhancement

C++ Code Cleanup

• Removed legacy commented code: Cleaned up all C++ source files (gkw.cpp, bkw.cpp, kkw.cpp, ekw.cpp, kw.cpp, bpmc.cpp, beta_.cpp) by removing old commented-out implementations that were kept for reference.
• Code formatting: Improved R wrapper formatting with consistent indentation and alignment in .Call() invocations and roxygen examples.

New Test Suites

• Analytical derivatives validation (test-derivatives-validation.R):
  • 70 comprehensive tests validating gradient (gr*) and Hessian (hs*) functions
  • Compares analytical derivatives against numerical differentiation via numDeriv
  • Covers all 7 subfamilies: GKw, BKw, KKw, EKw, Mc, Kw, Beta
  • Multiple parameter configurations per subfamily for robustness
• MLE performance benchmarks (test-mle-performance.R):
  • Compares optimization efficiency across three scenarios: numerical-only, analytical gradient, and analytical gradient + Hessian
  • Validates that analytical derivatives provide equivalent or better accuracy
  • Tests convergence rates and computational time across all distribution families

JOSS Paper

• Added paper for JOSS submission (inst/paper/):
  • Complete manuscript describing the package’s statistical framework
  • Comprehensive bibliography with foundational references
  • Compiled PDF ready for submission

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gkwdist 1.1.1

CRAN release: 2025-11-27

Major Refactoring Release

This release represents a comprehensive refactoring of the entire package codebase, focusing on numerical stability, code consistency, and maintainability.

C++ Backend Overhaul

• Unified utility functions: Introduced utils.h header providing numerically stable implementations of critical functions:

  • log1mexp(): Stable computation of log(1 - exp(x)) using Mächler (2012) methodology
  • log1pexp(): Overflow-protected computation of log(1 + exp(x))
  • safe_log(), safe_exp(), safe_pow(): Protected arithmetic operations with graceful handling of edge cases
  • Vectorized versions (vec_safe_log, vec_log1mexp, etc.) for efficient array operations

• Consistent parameter validation: All distribution families now use dedicated parameter checkers (check_pars(), check_kw_pars(), check_ekw_pars(), etc.) that properly handle NaN, Inf, and boundary conditions.

• Complete documentation: All C++ source files now include comprehensive Doxygen-style documentation headers describing:

  • Mathematical formulas for PDF, CDF, quantile, and random generation
  • Parameter constraints and special cases
  • Numerical stability considerations
  • Relationship to parent GKw distribution

Bug Fixes

• Fixed critical bug in qgkw(): Corrected logic error where lower_tail transformation was incorrectly applied when log_p = TRUE. The probability is now properly converted to linear scale before tail adjustment.

• Fixed gradient calculation in grkkw(): Resolved issue where log_z was not recomputed after clamping z to minimum threshold, causing corrupted gradient values near boundaries.

• Fixed Hessian calculation in hsmc(): Corrected sign errors and formula for the lambda component of the Hessian matrix for the Beta-Power/McDonald distribution.

• Fixed gradient signs in grmc(): Ensured consistent computation of log-likelihood gradient before negation for optimization.

Code Quality Improvements

• Eliminated unused variables: Removed declared but unused constants (exp_threshold) and intermediate variables across all distribution files.

• Removed redundant calculations: Streamlined computations, notably in pgkw() where logarithm was computed twice for the same quantity.

• Simplified parameter recycling: Replaced double-modulo indexing pattern (idx = i % k; vec[idx % vec.n_elem]) with direct single-modulo access (vec[i % vec.n_elem]) in random generation functions.

• Standardized function signatures: All distribution functions now follow consistent patterns for parameter order, validation, and return value handling.

R Wrapper Layer

• Complete separation of R and C++ interfaces: All exported R functions now serve as wrappers around internal C++ implementations (.dgkw_cpp, .pgkw_cpp, etc.), providing:
  • Enhanced input validation with informative error messages
  • Consistent argument checking across all distribution families
  • Proper NA/NaN propagation
  • Documentation accessible via standard R help system

Distribution Families

All seven distribution families have been refactored with identical improvements:

Distribution	Parameters	File
Generalized Kumaraswamy (GKw)	α, β, γ, δ, λ	gkw.cpp
Kumaraswamy-Kumaraswamy (KKw)	α, β, δ, λ	kkw.cpp
Beta-Kumaraswamy (BKw)	α, β, γ, δ	bkw.cpp
Exponentiated Kumaraswamy (EKw)	α, β, λ	ekw.cpp
Beta-Power/McDonald (BP/Mc)	γ, δ, λ	bpmc.cpp
Kumaraswamy (Kw)	α, β	kw.cpp
Beta (GKw-style)	γ, δ	beta.cpp

Each family includes: density (d*), distribution (p*), quantile (q*), random generation (r*), negative log-likelihood (ll*), gradient (gr*), and Hessian (hs*) functions.

Technical Notes

• Minimum supported R version remains 3.5.0
• C++11 standard required (enabled via Rcpp plugin)
• Depends on RcppArmadillo for efficient linear algebra operations

Acknowledgments

Special thanks to the thorough code review process that identified subtle numerical issues in edge cases, particularly for extreme parameter values and observations near distribution boundaries.

gkwdist 1.0.7

gkwdist 1.0.5

Documentation Improvements

• Enhanced Examples for Likelihood Functions: All ll*, gr*, and hs* functions now include comprehensive examples demonstrating:

  • Maximum likelihood estimation with analytical gradients
  • Univariate profile likelihoods with confidence thresholds
  • 2D likelihood surfaces with confidence regions (90%, 95%, 99%)
  • Confidence ellipses with marginal intervals for parameter pairs
  • Numerical vs analytical derivative verification
  • Likelihood ratio tests and score tests

• Professional Visualization Standards:

  • Consistent color scheme across all examples
  • Grid-adaptive algorithms for computational efficiency
  • Base R only - no external dependencies required

• Complete Coverage: Enhanced documentation for all distribution families (Kw, EKw, KKw, GKw) covering 2 to 5 parameters

• Theoretical References: Documentation cites foundational work by Carrasco et al. (2010), Jones (2009), Kumaraswamy (1980), and standard inference theory from Casella & Berger (2002)

gkwdist 1.0.3

• README.md: Fix typos and faill link
  • Fix zzz.R file by removing useless texts

gkwdist 1.0.2

gkwdist 1.0.1

Major Improvements

Enhanced gkwgetstartvalues() Function

• NEW: Added family parameter to support all distribution families
  • Automatically returns correct number of parameters for each family
  • Family-specific initial value strategies for better convergence
  • Supported families: "gkw", "bkw", "kkw", "ekw", "mc", "kw", "beta"
  • Case-insensitive family names for user convenience

Documentation Enhancements

• README.md: Complete rewrite with mathematical rigor
  • All LaTeX formulas corrected and verified for proper rendering
  • Eight comprehensive examples using optim() with analytical gradients
  • Corrected function signatures: all ll*(), gr*(), and hs*() functions use (par, data) signature
  • Added performance benchmarks demonstrating 10-50× speedup with C++ implementation
  • Hierarchical structure diagram for all distribution families
  • Model selection workflow and practical guidelines
  • Removed all references to deprecated gkwfit() function

CRAN Submission Readiness

• DESCRIPTION: Fixed to meet CRAN requirements
  • Proper Authors@R field formatting
  • Removed unused dependencies (numDeriv)
  • Corrected package dependencies (RcppArmadillo only in LinkingTo)
  • Enhanced description with DOI references
  • Fixed maintainer email formatting

Bug Fixes

• Fixed function call signatures in all README examples to match actual implementation
• Corrected parameter passing in optimization examples (now consistently use (par, data))
• Fixed LaTeX rendering issues with \left/\right delimiters in GitHub Markdown

Testing

• NEW: Comprehensive test suite using testthat
  • 100+ tests covering all exported functions
  • Tests for all 7 distribution families (GKw, BKw, KKw, EKw, MC, Kw, Beta)
  • PDF, CDF, quantile, and random generation tests
  • Log-likelihood, gradient, and Hessian validation
  • Parameter recovery tests with MLE
  • Edge cases and boundary condition handling
  • Integration tests for PDF-CDF consistency

Performance

• All functions implemented in C++ for maximum computational efficiency
• Analytical derivatives (gradient and Hessian) provide exact computations
• Optimized numerical stability for extreme parameter values

Notes

• This is the initial CRAN submission
• Package focuses exclusively on distribution functions (no high-level fitting interface)
• Companion package gkwreg provides regression modeling capabilities
• All user-facing functions maintain backward compatibility
• C++ implementation uses RcppArmadillo for linear algebra operations
• Analytical functions use robust log-scale computations to prevent overflow/underflow
• Random generation uses inverse CDF method where closed-form solutions exist

gkwdist 0.1.0

New Features

• Initial CRAN release
• Generalized Kumaraswamy distribution (5 parameters)
• Six nested sub-families: Beta, Kumaraswamy, Exponentiated-Kumaraswamy, Kumaraswamy-Kumaraswamy, Beta-Kumaraswamy, and McDonald distributions
• Complete set of distribution functions (d/p/q/r)
• Log-likelihood, gradient, and Hessian functions for all families

Performance

• Optimized C++ implementation via Rcpp
• Vectorized operations for speed