% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/dist_functions.R
\name{BetaDanish}
\alias{BetaDanish}
\alias{dbetadanish}
\alias{pbetadanish}
\alias{qbetadanish}
\alias{rbetadanish}
\alias{hbetadanish}
\title{The 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{
\item{x, q}{Vector of quantiles (time points).}

\item{a}{Shape parameter (beta generator). Set `a = 1` for the 3-parameter submodel.}

\item{b}{Shape parameter (beta generator / tail weight).}

\item{c}{Shape parameter (baseline shape).}

\item{k}{Scale parameter (baseline scale).}

\item{log, log.p}{Logical; if TRUE, probabilities/densities are given as log.}

\item{lower.tail}{Logical; if TRUE (default), probabilities are P[X <= x], otherwise P[X > x].}

\item{p}{Vector of probabilities.}

\item{n}{Number of observations to generate.}
}
\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.
}
\description{
Density, distribution function, quantile function, hazard function, and
random generation for the four-parameter Beta-Danish distribution.
}
\details{
The Beta-Danish distribution is a highly flexible lifetime distribution capable
of modeling decreasing, increasing, unimodal, and bathtub-shaped hazard rates.
}
\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)

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