dpldd gives the density, ppldd gives the distribution
function, qpldd gives the quantile function and rpldd generates
random deviates.
Arguments
x, q
vector of quantiles.
alpha, beta, theta
are parameters.
log, log.p
logical; if TRUE, probabilities p are given as log(p).
lower.tail
logical; if TRUE (default), probabilities are
\(P\left[ X\leq x\right]\), otherwise, \(P\left[ X>x\right] \).
p
vector of probabilities.
n
number of observations. If length(n) > 1, the length is taken
to be the number required.
Details
A Power Log Dagum Distribution with parameters \(\alpha\), \(\beta\) and
\(\theta\), has density
$$f\left( x\right) =\alpha
\left( \beta +\theta \left\vert x\right\vert^{\beta -1}
\right) e^{-\left( \beta x+sign\left( x\right)
\left( \theta/\beta \right) \left\vert
x\right\vert ^{\beta }\right) ~}~\left(1+e^{-\left( \beta x+sign
\left( x\right)\left( \theta /\beta \right)
\left\vert x\right\vert ^{\beta }\right) }
\right) ^{-\left( \alpha +1\right)},$$
where
$$x\in \mathbb{R},~\beta \in \mathbb{R},~\alpha >0~and~\theta \geq 0$$
References
Bakouch, H. S., Khan, M. N., Hussain, T. ve Chesneau, C., 2019,
A power log-Dagum distribution: estimation and applications, Journal of
Applied Statistics, 46 (5), 874-892.