zouweibull: Zero-or-One unit-Weibull distribution

In AndrMenezes/uwquantreg: unit-Weibull quantile regression

Description

Density function, distribution function, quantile function, random number generation function for the zero-or-one unit-Weibull distribution re-parametrized in terms of the τth quantile.

Usage

dzouweibull(x, mu, phi, tau, nu, inflation, log = FALSE)

pzouweibull(q, mu, phi, tau, nu, inflation, lower.tail = TRUE, log.p = FALSE)

qzouweibull(p, mu, phi, tau, nu, inflation, lower.tail = TRUE, log.p = FALSE)

rzouweibull(n, mu, phi, tau, nu, inflation)

Arguments

x, q	vector of positive quantiles.
mu	location parameter indicating the tau-quantile τ \in (0, 1).
phi	nonnegative shape parameter.
tau	the parameter to specify which quantile use in the parametrization.
nu	probability of inflation.
inflation	specify the zero (0) or the one (1) inflation.
log, log.p	logical; If TRUE, probabilities p are given as log(p).
lower.tail	logical; If TRUE, (default), P(X ≤q 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.

Value

dzouweibull gives the density, pzouweibull gives the distribution function, qzouweibull gives the quantile function and rzouweibull generates random deviates.

Invalid arguments will return an error message.

Author(s)

André Felipe B. Menezes [e-mail]

References

Mazucheli, J., Menezes, A. F. B and Ghitany, M. E. (2018). The unit-Weibull distribution and associated inference. Journal of Applied Probability and Statistics 13 (2), 1–22.

Mazucheli, J., Menezes, A. F. B., Fernandes, L. B., Oliveira, R. P., Ghitany, M. E., 2020. The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modelling of quantiles conditional on covariates. Jounal of Applied Statistics 47 (6), 954–974.

See Also

uweibull.

Examples

set.seed(6969)
x <- rzouweibull(n = 1e4, mu = 0.5, phi = 1.5, tau = 0.5, nu = 0.3, inflation = 1)
R <- range(x)
S <- seq(from = R[1], to = R[2], l = 1000)
plot(ecdf(x))
lines(S, pzouweibull(q = S, mu = 0.5, phi = 1.5, tau = 0.5, nu = 0.3, inflation = 1), col = 2)
plot(quantile(x, probs = S), type = "l")
lines(qzouweibull(p = S, mu = 0.5, phi = 1.5, tau = 0.5, nu = 0.3, inflation = 1), col = 2)

probs <- c(0.1, 0.2, 0.5, 0.7, 0.9)
(p <- pzouweibull(q = probs, mu = 0.1, phi = 2, tau = 0.5, nu = 0.5, inflation = 1))
qzouweibull(p, mu = 0.1, phi = 2, tau = 0.5, nu = 0.5, inflation = 1)

(p <- pzouweibull(q = probs, mu = 0.1, phi = 2, tau = 0.5, nu = 0.5, inflation = 0))
qzouweibull(p, mu = 0.1, phi = 2, tau = 0.5, nu = 0.5, inflation = 0)

AndrMenezes/uwquantreg documentation built on July 8, 2020, 2:33 p.m.