pldd {new.dist}

Power Log Dagum Distribution

Description

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.

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

Value

dpldd gives the density, ppldd gives the distribution function, qpldd gives the quantile function and rpldd generates random deviates.

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)
ppldd(1,alpha=2,beta=3,theta=4)
qpldd(.8,alpha=2,beta=3,theta=4)
rpldd(10,alpha=2,beta=3,theta=4)