Density, distribution function, quantile function and random generation for a Power Log Dagum distribution.
Usage
dpldd(x, alpha, beta, theta, log = FALSE)
ppldd(q, alpha, beta, theta, lower.tail = TRUE, log.p = FALSE)
qpldd(p, alpha, beta, theta, lower.tail = TRUE)
rpldd(n, alpha, beta, theta)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.
Value
dpldd gives the density, ppldd gives the distribution
function, qpldd gives the quantile function and rpldd generates
random deviates.
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 $$x\in \mathbb{R},~\beta \in \mathbb{R},~\alpha >0~and~\theta \geq 0$$
Note
The distributions hazard function $$h\left( x\right) =\frac{\alpha \left( \beta +\theta \left\vert x\right\vert^{\beta -1} \right) e^{-\left( \beta x+sign\left( x\right) \left( \theta/\beta \right) \left\vert x\right\vert ^{\beta }\right) }\left( 1+e^{-\left(\beta x+sign \left( x\right) \left( \theta /\beta \right) \left\vert x \right\vert ^{\beta }\right) }\right) ^{-\left(\alpha +1\right) }} {1-\left( 1+e^{-\left( \beta x+sign\left( x\right) \left( \theta / \beta \right) \left\vert x\right\vert ^{\beta }\right) } \right) ^{-\alpha }} .$$
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.
Examples
library(new.dist)
dpldd(1, alpha=2, beta=3, theta=4)
#> [1] 0.1766842
ppldd(1,alpha=2,beta=3,theta=4)
#> [1] 0.9742603
qpldd(.8,alpha=2,beta=3,theta=4)
#> [1] 0.6109249
rpldd(10,alpha=2,beta=3,theta=4)
#> [1] 0.374601489 0.195777288 0.467856947 0.899835959 -0.365719023
#> [6] 0.424477997 0.311789087 0.605405418 -0.004434866 0.060065088