ughne | R Documentation |
Density function, distribution function, quantile function and random number generation function
for the unit-Half-Normal-E distribution reparametrized in terms of the \tau
-th quantile, \tau \in (0, 1)
.
dughne(x, mu, theta, tau = 0.5, log = FALSE)
pughne(q, mu, theta, tau = 0.5, lower.tail = TRUE, log.p = FALSE)
qughne(p, mu, theta, tau = 0.5, lower.tail = TRUE, log.p = FALSE)
rughne(n, mu, theta, tau = 0.5)
x, q |
vector of positive quantiles. |
mu |
location parameter indicating the |
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 |
vector of probabilities. |
n |
number of observations. If |
Probability density function
f(y\mid \alpha ,\theta )=\sqrt{\frac{2}{\pi }}\frac{\theta }{y\left[ -\log\left( y\right) \right] }\left( -{\frac{\log \left( y\right) }{\alpha }} \right)^{\theta }\mathrm{\exp }\left\{ -\frac{1}{2}\left[ -{\frac{\log \left( y\right) }{\alpha }}\right]^{2\theta }\right\}
Cumulative distribution function
F(y\mid \alpha ,\theta )=2\Phi \left[ -\left( -{\frac{\log \left( y\right) }{\alpha }}\right)^{\theta }\right]
Quantile function
Q(\tau \mid \alpha ,\theta )=\exp \left\{ -\alpha \left[ -\Phi^{-1}\left(\frac{\tau }{2}\right) \right]^{\frac{1}{\theta }}\right\}
Reparameterization
\alpha=g^{-1}(\mu )=-\log \left( \mu \right) \left[ -\Phi^{-1}\left( \frac{\tau }{2}\right) \right]^{-\frac{1}{\theta }}
dughne
gives the density, pughne
gives the distribution function,
qughne
gives the quantile function and rughne
generates random deviates.
Invalid arguments will return an error message.
Josmar Mazucheli jmazucheli@gmail.com
André F. B. Menezes andrefelipemaringa@gmail.com
Korkmaz, M. C., (2020). The unit generalized half normal distribution: A new bounded distribution with inference and application. University Politehnica of Bucharest Scientific, 82(2), 133–140.
set.seed(123)
x <- rughne(n = 1000, mu = 0.5, theta = 2, tau = 0.5)
R <- range(x)
S <- seq(from = R[1], to = R[2], by = 0.01)
hist(x, prob = TRUE, main = 'unit-Half-Normal-E')
lines(S, dughne(x = S, mu = 0.5, theta = 2, tau = 0.5), col = 2)
plot(ecdf(x))
lines(S, pughne(q = S, mu = 0.5, theta = 2, tau = 0.5), col = 2)
plot(quantile(x, probs = S), type = "l")
lines(qughne(p = S, mu = 0.5, theta = 2, tau = 0.5), col = 2)
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