leeg {unitquantreg}R Documentation

The Log-extended exponential-geometric distribution

Description

Density function, distribution function, quantile function and random number generation function for the Log-extended exponential-geometric distribution reparametrized in terms of the \tau-th quantile, \tau \in (0, 1).

Usage

dleeg(x, mu, theta, tau = 0.5, log = FALSE)

pleeg(q, mu, theta, tau = 0.5, lower.tail = TRUE, log.p = FALSE)

qleeg(p, mu, theta, tau = 0.5, lower.tail = TRUE, log.p = FALSE)

rleeg(n, mu, theta, tau = 0.5)

Arguments

x, q

vector of positive quantiles.

mu

location parameter indicating the \tau-th quantile, \tau \in (0, 1).

theta

nonnegative shape parameter.

tau

the parameter to specify which quantile is to be used.

log, log.p

logical; If TRUE, probabilities p are given as log(p).

lower.tail

logical; If TRUE, (default), P(X \leq{x}) are returned, otherwise P(X > x).

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

Details

Probability density function

f(y\mid \alpha ,\theta )=\frac{\theta \left( 1+\alpha \right) y^{\theta -1}}{\left( 1+\alpha y^{\theta }\right) ^{2}}

Cumulative distribution function

F(y\mid \alpha ,\theta )=\frac{\left( 1+\alpha \right) y^{\theta }}{1+\alpha y^{\theta }}

Quantile function

Q(\tau \mid \alpha ,\theta )=\left[ \frac{\tau }{1+\alpha \left( 1-\tau\right) }\right] ^{\frac{1}{\theta }}

Reparameterization

\alpha=g^{-1}(\mu )=-\frac{1-\tau \mu ^{\theta }}{\left( 1-\tau \right) }

Value

dleeg gives the density, pleeg gives the distribution function, qleeg gives the quantile function and rleeg generates random deviates.

Invalid arguments will return an error message.

Author(s)

Josmar Mazucheli jmazucheli@gmail.com

André F. B. Menezes andrefelipemaringa@gmail.com

References

Jodrá, P. and Jiménez-Gamero, M. D., (2020). A quantile regression model for bounded responses based on the exponential-geometric distribution. Revstat - Statistical Journal, 18(4), 415–436.

Examples

set.seed(123)
x <- rleeg(n = 1000, mu = 0.5, theta = 1.5, tau = 0.5)
R <- range(x)
S <- seq(from = R[1], to = R[2], by =  0.01)
hist(x, prob = TRUE, main = 'Log-extended exponential-geometric')
lines(S, dleeg(x = S, mu = 0.5, theta = 1.5, tau = 0.5), col = 2)
plot(ecdf(x))
lines(S, pleeg(q = S, mu = 0.5, theta = 1.5, tau = 0.5), col = 2)
plot(quantile(x, probs = S), type = "l")
lines(qleeg(p = S, mu = 0.5, theta = 1.5, tau = 0.5), col = 2)

[Package unitquantreg version 0.0.6 Index]