The hardware and bandwidth for this mirror is donated by METANET, the Webhosting and Full Service-Cloud Provider.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]metanet.ch.

gkwdist: Generalized Kumaraswamy Distribution Family

Overview

gkwdist implements the Generalized Kumaraswamy (GKw) distribution family and its seven nested sub-models for bounded continuous data on \((0,1)\). All functions are implemented in C++ via RcppArmadillo for maximum computational efficiency.

Key Features: - Seven flexible distributions for proportions, rates, and bounded data - Standard R distribution API: d*, p*, q*, r* - Analytical log-likelihood, gradient, and Hessian functions - All functions implemented in C++ for optimal performance - 10-50× faster than equivalent R implementations - Numerically stable for extreme parameter values

Installation

# Install from GitHub
# install.packages("devtools")
devtools::install_github("evandeilton/gkwdist")

The Distribution Family

Complete Function Table

Function Types

Distribution Functions (C++ implementation with R interface):

• d*() — Probability density function (PDF)
• p*() — Cumulative distribution function (CDF)
• q*() — Quantile function (inverse CDF)
• r*() — Random number generation

Analytical Functions for Maximum Likelihood (C++ implementation):

All analytical functions use the signature: function(par, data) where par is a numeric vector of parameters.

• ll*(par, data) — Negative log-likelihood:

\[-\ell(\boldsymbol{\theta}; \mathbf{x}) = -\sum_{i=1}^n \log f(x_i; \boldsymbol{\theta})\]

• gr*(par, data) — Negative gradient (negative score vector):

\[-\nabla_{\boldsymbol{\theta}} \ell(\boldsymbol{\theta}; \mathbf{x})\]

• hs*(par, data) — Negative Hessian matrix:

\[-\nabla^2_{\boldsymbol{\theta}} \ell(\boldsymbol{\theta}; \mathbf{x})\]

Note: These functions return negative values to facilitate direct use with optimization routines like optim(), which perform minimization by default.

Mathematical Specification

Notation: All parameters are strictly positive (\(\alpha, \beta, \gamma, \delta, \lambda > 0\)); support \(x \in (0, 1)\). The beta function is \(B(a,b) = \Gamma(a)\Gamma(b)/\Gamma(a+b)\), and the regularized incomplete beta function is \(I_z(a,b) = B_z(a,b)/B(a,b)\) where \(B_z(a,b) = \int_0^z t^{a-1}(1-t)^{b-1}dt\).

1. Generalized Kumaraswamy (GKw)

Parameters: \(\alpha, \beta, \gamma, \delta, \lambda > 0\)

PDF:

\[f_{\text{GKw}}(x; \alpha, \beta, \gamma, \delta, \lambda) = \frac{\lambda \alpha \beta}{B(\gamma, \delta)} x^{\alpha-1} (1-x^\alpha)^{\beta-1} \left[1-(1-x^\alpha)^\beta\right]^{\gamma\lambda-1} \left\{1-\left[1-(1-x^\alpha)^\beta\right]^\lambda\right\}^{\delta-1}\]

CDF:

\[F_{\text{GKw}}(x; \alpha, \beta, \gamma, \delta, \lambda) = I_{[1-(1-x^\alpha)^\beta]^\lambda}(\gamma, \delta)\]

Quantile: Numerical inversion of the CDF via root-finding algorithms.

Moments: Analytical expressions not available in closed form. Numerical integration or simulation methods required.

2. Beta-Kumaraswamy (BKw)

Relationship: Special case of GKw with \(\lambda = 1\)

PDF:

\[f_{\text{BKw}}(x; \alpha, \beta, \gamma, \delta) = \frac{\alpha \beta}{B(\gamma, \delta)} x^{\alpha-1} (1-x^\alpha)^{\beta-1} \left[1-(1-x^\alpha)^\beta\right]^{\gamma-1} \left\{1-\left[1-(1-x^\alpha)^\beta\right]\right\}^{\delta-1}\]

Simplifying:

\[f_{\text{BKw}}(x; \alpha, \beta, \gamma, \delta) = \frac{\alpha \beta}{B(\gamma, \delta)} x^{\alpha-1} (1-x^\alpha)^{\beta-1} \left[1-(1-x^\alpha)^\beta\right]^{\gamma-1} (1-x^\alpha)^{\beta(\delta-1)}\]

\[= \frac{\alpha \beta}{B(\gamma, \delta)} x^{\alpha-1} (1-x^\alpha)^{\beta\delta-1} \left[1-(1-x^\alpha)^\beta\right]^{\gamma-1}\]

CDF:

\[F_{\text{BKw}}(x; \alpha, \beta, \gamma, \delta) = I_{1-(1-x^\alpha)^\beta}(\gamma, \delta)\]

Quantile: Numerical inversion via root-finding. For the inverse:

\[u = I_y(\gamma, \delta) \quad \text{where} \quad y = 1-(1-x^\alpha)^\beta\]

Solving for \(x\):

\[x = \left[1-\left(1-I_u^{-1}(\gamma, \delta)\right)^{1/\beta}\right]^{1/\alpha}\]

3. Kumaraswamy-Kumaraswamy (KKw)

Relationship: Special case of GKw with \(\gamma = 1\)

PDF:

\[f_{\text{KKw}}(x; \alpha, \beta, \delta, \lambda) = \alpha \beta \delta \lambda \, x^{\alpha-1} (1-x^\alpha)^{\beta-1} \left[1-(1-x^\alpha)^\beta \right]^{\lambda-1} \left\{1-\left[1-(1-x^\alpha)^\beta \right]^\lambda\right\}^{\delta-1}\]

CDF:

\[F_{\text{KKw}}(x; \alpha, \beta, \delta, \lambda) = 1 - \left\{1-\left[1-(1-x^\alpha)^\beta\right]^\lambda\right\}^\delta\]

Quantile (closed-form):

\[Q_{\text{KKw}}(p; \alpha, \beta, \delta, \lambda) = \left[1 - \left(1 - \left[1-(1-p)^{1/\delta}\right]^{1/\lambda}\right)^{1/\beta}\right]^{1/\alpha}\]

Moments: Analytical expressions not available in closed form.

4. Exponentiated Kumaraswamy (EKw)

Relationship: Special case of GKw with \(\gamma = \delta = 1\)

PDF:

\[f_{\text{EKw}}(x; \alpha, \beta, \lambda) = \lambda \alpha \beta \, x^{\alpha-1} (1-x^\alpha)^{\beta-1} \left[1-(1-x^\alpha)^\beta \right]^{\lambda-1}\]

CDF:

\[F_{\text{EKw}}(x; \alpha, \beta, \lambda) = \left[1-(1-x^\alpha)^\beta \right]^\lambda\]

Quantile (closed-form):

\[Q_{\text{EKw}}(p; \alpha, \beta, \lambda) = \left[1-\left(1-p^{1/\lambda}\right)^{1/\beta}\right]^{1/\alpha}\]

Moments:

\[\mathbb{E}(X^r) = \lambda \sum_{k=0}^{\infty} \frac{(-1)^k \binom{\lambda}{k+1}}{k+1} \cdot \beta B\left(1 + \frac{r}{\alpha}, (k+1)\beta\right)\]

where the binomial coefficient is generalized: \(\binom{\lambda}{k+1} = \frac{\lambda(\lambda-1)\cdots(\lambda-k)}{(k+1)!}\).

5. McDonald (Beta Power)

Relationship: Special case of GKw with \(\alpha = \beta = 1\)

PDF:

\[f_{\text{MC}}(x; \gamma, \delta, \lambda) = \frac{\lambda}{B(\gamma, \delta)} x^{\gamma\lambda-1} (1-x^\lambda)^{\delta-1}\]

CDF:

\[F_{\text{MC}}(x; \gamma, \delta, \lambda) = I_{x^\lambda}(\gamma, \delta)\]

Quantile:

\[Q_{\text{MC}}(p; \gamma, \delta, \lambda) = \left[I_p^{-1}(\gamma, \delta)\right]^{1/\lambda}\]

where \(I_p^{-1}(\gamma, \delta)\) is the inverse regularized incomplete beta function (quantile function of the Beta distribution).

Moments:

\[\mathbb{E}(X^r) = \frac{B(\gamma + r/\lambda, \delta)}{B(\gamma, \delta)}\]

which is valid for \(r/\lambda > -\gamma\).

6. Kumaraswamy (Kw)

Relationship: Special case of GKw with \(\gamma = \delta = \lambda = 1\)

PDF:

\[f_{\text{Kw}}(x; \alpha, \beta) = \alpha \beta \, x^{\alpha-1} (1-x^\alpha)^{\beta-1}\]

CDF:

\[F_{\text{Kw}}(x; \alpha, \beta) = 1 - (1-x^\alpha)^\beta\]

Quantile (closed-form):

\[Q_{\text{Kw}}(p; \alpha, \beta) = \left[1-(1-p)^{1/\beta} \right]^{1/\alpha}\]

Moments:

\[\mathbb{E}(X^r) = \beta B\left(1 + \frac{r}{\alpha}, \beta\right) = \frac{\beta \, \Gamma(1+r/\alpha) \, \Gamma(\beta)}{\Gamma(1+r/\alpha+\beta)}\]

which is valid for \(r/\alpha > -1\).

Special Cases:

\[\mathbb{E}(X) = \frac{\beta \, \Gamma(1+1/\alpha) \, \Gamma(\beta)}{\Gamma(1+1/\alpha+\beta)}\]

\[\mathbb{E}(X^2) = \frac{\beta \, \Gamma(1+2/\alpha) \, \Gamma(\beta)}{\Gamma(1+2/\alpha+\beta)}\]

\[\text{Var}(X) = \mathbb{E}(X^2) - [\mathbb{E}(X)]^2\]

7. Beta

Relationship: Special case of GKw with \(\alpha = \beta = \lambda = 1\)

PDF:

\[f_{\text{Beta}}(x; \gamma, \delta) = \frac{1}{B(\gamma, \delta)} x^{\gamma-1} (1-x)^{\delta-1}\]

CDF:

\[F_{\text{Beta}}(x; \gamma, \delta) = I_x(\gamma, \delta)\]

Quantile:

\[Q_{\text{Beta}}(p; \gamma, \delta) = I_p^{-1}(\gamma, \delta)\]

Moments:

\[\mathbb{E}(X^r) = \frac{B(\gamma+r, \delta)}{B(\gamma, \delta)} = \frac{\Gamma(\gamma+r) \, \Gamma(\delta) \, \Gamma(\gamma+\delta)}{\Gamma(\gamma) \, \Gamma(\gamma+\delta+r) \, \Gamma(\delta)}\]

\[\mathbb{E}(X) = \frac{\gamma}{\gamma+\delta}\]

\[\text{Var}(X) = \frac{\gamma\delta}{(\gamma+\delta)^2(\gamma+\delta+1)}\]

Hierarchical Structure

                              GKw(α, β, γ, δ, λ)
                              /               \
                           λ = 1             γ = 1
                            /                    \
                   BKw(α, β, γ, δ)         KKw(α, β, δ, λ)
                         |                          |
                     α = β = 1                    δ = 1
                         |                          |
                    MC(γ, δ, λ)              EKw(α, β, λ)
                         |                          |
                      λ = 1                    γ = δ = 1
                         |                          |
                    Beta(γ, δ)                   Kw(α, β)

Note: The Beta distribution is obtained from MC by setting \(\lambda = 1\), or from GKw by setting \(\alpha = \beta = \lambda = 1\). The Kumaraswamy distribution is obtained from EKw by setting \(\lambda = 1\), or from GKw by setting \(\gamma = \delta = \lambda = 1\).

Usage Examples

Example 1: Basic Distribution Functions

library(gkwdist)

# Set parameters
alpha <- 2; beta <- 3; gamma <- 1.5; delta <- 2; lambda <- 1.2
x <- seq(0.01, 0.99, length.out = 100)

# Density
dens <- dgkw(x, alpha, beta, gamma, delta, lambda)

# CDF
cdf <- pgkw(x, alpha, beta, gamma, delta, lambda)

# Quantiles
q <- qgkw(c(0.25, 0.5, 0.75), alpha, beta, gamma, delta, lambda)
print(q)

# Random generation
set.seed(123)
random_sample <- rgkw(1000, alpha, beta, gamma, delta, lambda)

# Visualization
par(mfrow = c(1, 2))
plot(x, dens, type = "l", lwd = 2, col = "blue",
     main = "GKw PDF", xlab = "x", ylab = "Density")
grid()

plot(x, cdf, type = "l", lwd = 2, col = "red",
     main = "GKw CDF", xlab = "x", ylab = "F(x)")
grid()

Example 2: Comparing Distribution Families

library(gkwdist)

par(mfrow = c(1,1), mar = c(3,3,2,2))

x <- seq(0.001, 0.999, length.out = 500)

# Compute densities for all families
d_gkw  <- dgkw(x, 2, 3, 1.5, 2, 1.2)
d_bkw  <- dbkw(x, 2, 3, 1.5, 2)
d_kkw  <- dkkw(x, 2, 3, 2, 1.2)
d_ekw  <- dekw(x, 2, 3, 1.5)
d_mc   <- dmc(x, 2, 3, 1.2)
d_kw   <- dkw(x, 2, 5)
d_beta <- dbeta_(x, 2, 3)

# Plot comparison
plot(x, d_gkw, type = "l", lwd = 2, col = "black",
     ylim = c(0, max(d_gkw, d_bkw, d_kkw, d_ekw, d_mc, d_kw, d_beta)),
     main = "Distribution Family Comparison",
     xlab = "x", ylab = "Density")
lines(x, d_bkw, lwd = 2, col = "red")
lines(x, d_kkw, lwd = 2, col = "blue")
lines(x, d_ekw, lwd = 2, col = "green")
lines(x, d_mc,  lwd = 2, col = "purple")
lines(x, d_kw,  lwd = 2, col = "orange")
lines(x, d_beta, lwd = 2, col = "brown")
legend("topright",
       legend = c("GKw", "BKw", "KKw", "EKw", "MC", "Kw", "Beta"),
       col = c("black", "red", "blue", "green", "purple", "orange", "brown"),
       lwd = 2, cex = 0.85)
grid()

Example 3: Maximum Likelihood Estimation Using optim()

library(gkwdist)

# Generate synthetic data from Kumaraswamy distribution
set.seed(2024)

n <- 2000
true_alpha <- 2.5
true_beta  <- 3.5
data <- rkw(n, true_alpha, true_beta)

# Get starting values
par_ini <- gkwgetstartvalues(data, family = "kw", n_starts = 2)

# Optimization using BFGS with analytical gradient
fit <- optim(
  par = par_ini,
  fn = llkw,  # Negative log-likelihood function
  gr = grkw,  # Negative gradient (negative score function)
  data = data,
  method = "BFGS",
  hessian = TRUE
)

# Standard errors from observed information matrix
se <- sqrt(diag(solve(fit$hessian)))

# 95% Confidence intervals
ci <- cbind(
  Lower    = fit$par - 1.96 * se,
  Estimate = fit$par,
  Upper    = fit$par + 1.96 * se
)
rownames(ci) <- c("alpha", "beta")

cat("True parameters:    ", true_alpha, true_beta, "\n")
cat("Estimated parameters:", fit$par, "\n\n")
print(ci)

Example 4: Goodness-of-Fit Diagnostic Plot

library(gkwdist)

# Using fitted model from Example 3
x_grid <- seq(0.001, 0.999, length.out = 200)

# Fitted density
fitted_dens <- dkw(x_grid, fit$par[1], fit$par[2])

# True density (for comparison)
true_dens <- dkw(x_grid, true_alpha, true_beta)

# Diagnostic plot
hist(data, breaks = 30, probability = TRUE,
     col = "lightgray", border = "white",
     main = "Kumaraswamy Distribution Fit",
     xlab = "Data", ylab = "Density")
lines(x_grid, fitted_dens, col = "red", lwd = 2, lty = 1)
lines(x_grid, true_dens, col = "blue", lwd = 2, lty = 2)
legend("topright",
       legend = c("Observed Data", "Fitted Model", "True Model"),
       col = c("gray", "red", "blue"),
       lwd = c(10, 2, 2), lty = c(1, 1, 2))
grid()

Example 5: Model Selection Using AIC and BIC

library(gkwdist)

# Generate data from Exponentiated Kumaraswamy
set.seed(456)
n <- 1500
data <- rekw(n, alpha = 2, beta = 3, lambda = 1.5)

# Define competing models
models <- list(
  Beta = list(
    nll = function(par) llbeta(par, data),
    gr = function(par) grbeta(par, data),
    start = gkwgetstartvalues(data, family = "beta"),
    npar = 2
  ),
  Kw = list(
    nll = function(par) llkw(par, data),
    gr = function(par) grkw(par, data),
    start = gkwgetstartvalues(data, family = "kw"),
    npar = 2
  ),
  EKw = list(
    nll = function(par) llekw(par, data),
    gr = function(par) grekw(par, data),
    start = gkwgetstartvalues(data, family = "ekw"),
    npar = 3
  ),
  MC = list(
    nll = function(par) llmc(par, data),
    gr = function(par) grmc(par, data),
    start = gkwgetstartvalues(data, family = "mc"),
    npar = 3
  )
)

# Fit all models using optim with analytical gradients
fits <- lapply(models, function(m) {
  optim(par = m$start, fn = m$nll, gr = m$gr, method = "BFGS")
})

# Extract log-likelihoods and compute information criteria
loglik <- sapply(fits, function(f) -f$value)
k <- sapply(models, `[[`, "npar")

results <- data.frame(
  Model  = names(models),
  Coefs  = sapply(fits, function(f) paste0(round(f$par, 3), collapse = "|")),
  LogLik = round(loglik, 2),
  nPar   = k,
  AIC    = round(-2 * loglik + 2 * k, 2),
  BIC    = round(-2 * loglik + k * log(n), 2)
)

# Sort by AIC
results <- results[order(results$AIC), ]
print(results, row.names = FALSE)
cat("\nBest model by AIC:", results$Model[1], "\n")

Example 6: Using Analytical Functions Directly

library(gkwdist)

# Generate data from EKw
set.seed(789)
n <- 1000
data <- rekw(n, alpha = 2, beta = 3, lambda = 1.5)
params <- c(2, 3, 1.5)

# Compute analytical functions at true parameters
nll <- llekw(params, data)
neg_score <- grekw(params, data)
neg_hess <- hsekw(params, data)

# Fisher information matrix (negative of negative Hessian = Hessian)
fisher <- -neg_hess

# Asymptotic standard errors
se <- sqrt(diag(solve(fisher)))
names(se) <- c("alpha", "beta", "lambda")

cat("Negative log-likelihood:", nll, "\n")
cat("\nNegative score vector (should be close to zero at true params):\n")
print(neg_score)
cat("\nNegative Hessian matrix:\n")
print(neg_hess)
cat("\nFisher Information matrix:\n")
print(fisher)
cat("\nAsymptotic standard errors:\n")
print(se)

Example 7: Q-Q Plot for Model Validation

library(gkwdist)

# Generate data and fit model
set.seed(101)
n <- 2000
data <- rkw(n, alpha = 2, beta = 3)

# Fit using optim
fit <- optim(
  par = c(1, 1),
  fn = function(par) llkw(par, data),
  gr = function(par) grkw(par, data),
  method = "BFGS"
)

# Theoretical quantiles
p <- ppoints(n)
theoretical_q <- qkw(p, fit$par[1], fit$par[2])

# Empirical quantiles
empirical_q <- sort(data)

# Q-Q plot
plot(theoretical_q, empirical_q,
     xlab = "Theoretical Quantiles",
     ylab = "Empirical Quantiles",
     main = "Q-Q Plot: Kumaraswamy Distribution",
     pch = 19, col = rgb(0, 0, 1, 0.5))
abline(0, 1, col = "red", lwd = 2, lty = 2)
grid()

Example 8: Fitting GKw (Full Model) Using optim()

library(gkwdist)

# Generate data from GKw
set.seed(2025)
n <- 10000
true_params <- c(alpha = 2, beta = 2.5, gamma = 1.5, delta = 2, lambda = 1.3)
data <- rgkw(n, true_params[1], true_params[2], true_params[3],
             true_params[4], true_params[5])

# Get starting values
par_ini <- gkwgetstartvalues(data, family = "gkw", n_starts = 5)

# Fit using optim with analytical gradient
fit_gkw <- optim(
  par = par_ini, 
  fn = llgkw,    # Negative log-likelihood
  gr = grgkw,    # Negative gradient
  data = data,
  method = "BFGS",
  hessian = TRUE,
  control = list(maxit = 1000)
)

# Results
se <- sqrt(diag(solve(fit_gkw$hessian)))
estimates <- data.frame(
  Parameter = names(true_params),
  True = true_params,
  Estimate = fit_gkw$par,
  SE = se
)
print(estimates, digits = 4)

Example 9: Comparing Analytical vs Numerical Derivatives

library(gkwdist)

# Generate data
set.seed(999)
n <- 10000
data <- rkw(n, alpha = 2, beta = 3)
par <- c(2, 3)

# Negative analytical gradient
neg_grad_analytical <- grkw(par, data)

# Numerical gradient (using finite differences)
neg_grad_numerical <- numDeriv::grad(
  func = function(p) llkw(p, data),
  x = par
)

# Compare
comparison <- data.frame(
  Parameter = c("alpha", "beta"),
  Analytical = neg_grad_analytical,
  Numerical = neg_grad_numerical,
  Difference = abs(neg_grad_analytical - neg_grad_numerical)
)
print(comparison, digits = 8)

Performance Comparison

The C++ implementation provides substantial performance gains:

library(microbenchmark)

# Generate large dataset
n <- 10000
data <- rkw(n, 2, 3)

# Compare log-likelihood computation
benchmark <- microbenchmark(
  R_sum_log_d = -sum(log(dkw(data, 2, 3))),  # Manual negative log-likelihood
  Cpp_ll = llkw(c(2, 3), data),               # C++ negative log-likelihood
  times = 100
)

print(benchmark)
plot(benchmark)
# Typical results: C++ implementation is 10-50× faster

Why C++ Implementation Matters:

• Speed: Critical for maximum likelihood estimation with large datasets
• Numerical Stability: Better handling of extreme parameter values and edge cases
• Memory Efficiency: Optimized memory allocation in tight loops
• Scalability: Linear scaling with sample size
• Precision: Analytical derivatives are exact (up to floating-point precision)

When to Use Each Distribution

Model Selection Workflow:

1. Start with Beta and Kumaraswamy (2 parameters)
2. Check goodness-of-fit using Q-Q plots and formal tests
3. If inadequate, try EKw or MC (3 parameters)
4. For complex patterns, use BKw, KKw, or GKw (4-5 parameters)
5. Use AIC/BIC to balance fit quality and parsimony
6. Validate final model with residual diagnostics

References

• Cordeiro, G. M., & de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81(7), 883-898. doi:10.1080/00949650903530745

• Carrasco, J. M. F., Ferrari, S. L. P., & Cordeiro, G. M. (2010). A new generalized Kumaraswamy distribution. arXiv:1004.0911. arxiv.org/abs/1004.0911

• Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46(1-2), 79-88. doi:10.1016/0022-1694(80)90036-0

• Jones, M. C. (2009). Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages. Statistical Methodology, 6(1), 70-81. doi:10.1016/j.stamet.2008.04.001

• Lemonte, A. J., & Cordeiro, G. M. (2013). An extended Lomax distribution. Statistics, 47(4), 800-816. doi:10.1080/02331888.2011.568119

• Cordeiro, G. M., & Lemonte, A. J. (2011). The β-Birnbaum–Saunders distribution: An improved distribution for fatigue life modeling. Computational Statistics & Data Analysis, 55(3), 1445-1461. doi:10.1016/j.csda.2010.10.007

• McDonald, J. B. (1984). Some generalized functions for the size distribution of income. Econometrica, 52(3), 647-663. doi:10.2307/1913469

• Cordeiro, G. M., & Brito, R. S. (2012). The beta power distribution. Brazilian Journal of Probability and Statistics, 26(1), 88-112. doi:10.1214/10-BJPS124

Citation

citation("gkwdist")

@Manual{gkwdist2025,
  title  = {gkwdist: Generalized Kumaraswamy Distribution Family},
  author = {J. E. Lopes},
  year   = {2025},
  note   = {R package},
  url    = {https://github.com/evandeilton/gkwdist}
}

Author

J. E. Lopes
LEG - Laboratory of Statistics and Geoinformation
PPGMNE - Graduate Program in Numerical Methods in Engineering
Federal University of Paraná (UFPR), Brazil
Email: evandeilton@gmail.com

License

MIT License. See LICENSE file for details.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.