The hardware and bandwidth for this mirror is donated by dogado GmbH, the Webhosting and Full Service-Cloud Provider. Check out our Wordpress Tutorial.
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[@]dogado.de.
The BetaDanish package implements the four-parameter Beta-Danish distribution and its three-parameter Exponentiated Danish (ED) submodel for survival, reliability, and lifetime-data analysis. The distribution was introduced by Ahmad and Danish (2025) and offers a flexible alternative to classical lifetime models such as the Weibull, gamma, and log-normal, while accommodating monotonic, unimodal, and bathtub-shaped hazards within a single parametric family.
Beyond the core distribution, the package provides a comprehensive toolkit for modern survival modelling:
You can install the development version of BetaDanish from GitHub with:
# install.packages("devtools")
devtools::install_github("bilal-aiou/BetaDanish")Optional packages used by advanced modules (declared in
Suggests):
install.packages(c("MCMCpack", "coda", "cmprsk", "flexsurv", "MASS"))The Beta-Danish distribution is obtained by applying the beta-generated family of Eugene, Lee, and Famoye (2002) to the Danish baseline, whose cumulative distribution function and density are
\[G(z; c, k) = \left(\frac{kz}{1+kz}\right)^c, \qquad g(z; c, k) = ck\,(kz)^{c-1}(1+kz)^{-(c+1)}, \qquad z > 0,\]
with shape parameter \(c > 0\) and scale parameter \(k > 0\).
For a random variable \(Z \sim \text{BetaDanish}(a, b, c, k)\) with \(a, b, c, k > 0\), the CDF is the regularised incomplete beta function evaluated at the Danish CDF:
\[F_Z(z; a, b, c, k) = I_{G(z; c, k)}(a, b) = I_{(kz/(1+kz))^c}(a, b), \qquad z > 0,\]
where \(I_x(a, b) = B_x(a, b) / B(a, b)\) and \(B(a, b)\) is the beta function.
Differentiating the CDF yields the density
\[f_Z(z; a, b, c, k) = \frac{ck}{B(a, b)} \cdot \frac{(kz)^{ca - 1}}{(1 + kz)^{ca + 1}} \cdot \left[1 - \left(\frac{kz}{1 + kz}\right)^c\right]^{b - 1}, \qquad z > 0.\]
The case \(a = 1\) yields the three-parameter Exponentiated Danish (ED) submodel used throughout the case studies.
The package provides numerically stable d/p/q/r/h functions analogous to the base R distribution interface:
| Function | Purpose |
|---|---|
dbetadanish() |
Density (PDF) |
pbetadanish() |
Cumulative distribution (CDF) and survival |
qbetadanish() |
Quantile function |
rbetadanish() |
Random number generation |
hbetadanish() |
Hazard rate |
library(BetaDanish)
# 1. Evaluate the density, CDF, hazard
dbetadanish(x = 2, a = 1.5, b = 2, c = 3, k = 0.5)
pbetadanish(q = 2, a = 1.5, b = 2, c = 3, k = 0.5)
hbetadanish(x = 2, a = 1.5, b = 2, c = 3, k = 0.5)
# 2. Simulate data and fit a model
set.seed(123)
dat <- simulate_bd_data(n = 200, a = 1.5, b = 2, c = 3, k = 0.5,
censor_rate = 0.2)
fit <- fit_betadanish(survival::Surv(time, status) ~ 1, data = dat)
summary(fit)
# 3. Diagnostic plots
plot(fit, type = "all")
# 4. Compare against standard distributions
compare_distributions(fit)data("remission")
fit_bayes <- bayes_betadanish(
time = remission$time,
status = remission$status,
submodel = TRUE,
burnin = 2000,
mcmc = 5000,
seed = 1
)
print(fit_bayes)See the Bayesian Estimation vignette for full details.
data("brain_cancer")
fit_aft <- fit_bd_aft(
survival::Surv(Survtime, Survstatus) ~ Age + Grade + Surgery,
data = brain_cancer
)
summary(fit_aft)
plot(fit_aft) # Cox-Snell residual diagnosticBoth mixture and promotion-time cure models on the Exponentiated Danish kernel:
fit_cure <- fit_bd_cure(
formula_aft = survival::Surv(time, status) ~ 1,
formula_cure = ~ group,
data = mydata,
type = "mixture"
)
summary(fit_cure)fit_cr <- fit_bd_competing(time = time, cause = cause)
res <- cif_compare(fit_cr, plot = TRUE)
res$gray_testThe fitted Beta-Danish cumulative incidence functions are overlaid against the nonparametric Aalen-Johansen estimator, with Gray’s test reported for cause equality.
| Function | Property |
|---|---|
bd_entropy_shannon() |
Shannon (differential) entropy |
bd_order_stat_pdf() |
r-th order statistic density |
| Dataset | n | Description |
|---|---|---|
remission |
128 | Bladder cancer remission times |
carbon_fibres |
100 | Breaking stress of carbon fibres (Gba) |
transplant |
91 | Bone marrow transplant survival |
aarset |
50 | Aarset device failure times (bathtub hazard) |
leukemia |
23 | Acute myelogenous leukemia survival |
melanoma |
205 | Malignant melanoma post-surgery |
brain_cancer |
varies | Brain cancer survival with comorbidities |
The package ships with five comprehensive tutorials:
bayes_betadanish()Browse them with:
browseVignettes("BetaDanish")If you use BetaDanish in published work, please cite:
Ahmad, B., & Danish, M. Y. (2025). The Beta-Danish distribution for lifetime data analysis. Journal of Applied Mathematics, Statistics and Informatics, 21(1). https://doi.org/10.2478/jamsi-2025-0010
A BibTeX entry is available via:
citation("BetaDanish")Ahmad, B., & Danish, M. Y. (2025). The Beta-Danish distribution for lifetime data analysis. Journal of Applied Mathematics, Statistics and Informatics, 21(1). https://doi.org/10.2478/jamsi-2025-0010
Eugene, N., Lee, C., & Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics — Theory and Methods, 31(4), 497–512.
?fit_betadanish in Rvignette(package = "BetaDanish")Bilal Ahmad (maintainer) — Allama Iqbal Open University, Islamabad, Pakistan. bilalahmad.imcbh9@gmail.com
Muhammad Yameen Danish — Allama Iqbal Open University, Islamabad, Pakistan. yameen.danish@aiou.edu.pk
GPL-3
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.
Health stats visible at Monitor.