BetaDanish: The Beta-Danish Distribution

In BetaDanish: The Beta-Danish Distribution for Lifetime Data Analysis

The Beta-Danish Distribution

Description

Density, distribution function, quantile function, hazard function, and random generation for the four-parameter Beta-Danish distribution.

Usage

dbetadanish(x, a, b, c, k, log = FALSE)

pbetadanish(q, a, b, c, k, lower.tail = TRUE, log.p = FALSE)

qbetadanish(p, a, b, c, k, lower.tail = TRUE, log.p = FALSE)

rbetadanish(n, a, b, c, k)

hbetadanish(x, a, b, c, k, log = FALSE)

Arguments

x, q	Vector of quantiles (time points).
a	Shape parameter (beta generator). Set 'a = 1' for the 3-parameter submodel.
b	Shape parameter (beta generator / tail weight).
c	Shape parameter (baseline shape).
k	Scale parameter (baseline scale).
log, log.p	Logical; if TRUE, probabilities/densities are given as log.
lower.tail	Logical; if TRUE (default), probabilities are P[X <= x], otherwise P[X > x].
p	Vector of probabilities.
n	Number of observations to generate.

Details

The Beta-Danish distribution is a highly flexible lifetime distribution capable of modeling decreasing, increasing, unimodal, and bathtub-shaped hazard rates.

Value

'dbetadanish' gives the density, 'pbetadanish' gives the distribution function, 'qbetadanish' gives the quantile function, 'hbetadanish' gives the hazard function, and 'rbetadanish' generates random deviates.

References

Ahmad, B., & Danish, M. Y. (2026). Development and Characterization of a Flexible Three-Parameter Lifetime Distribution.

Examples

# Density
dbetadanish(x = 2, a = 1.5, b = 2, c = 3, k = 0.5)

# CDF
pbetadanish(q = 2, a = 1.5, b = 2, c = 3, k = 0.5)

# Hazard
hbetadanish(x = 2, a = 1.5, b = 2, c = 3, k = 0.5)

# Random generation
rbetadanish(n = 10, a = 1.5, b = 2, c = 3, k = 0.5)

BetaDanish documentation built on May 20, 2026, 5:07 p.m.