ughnx | R Documentation |
Density function, distribution function, quantile function and random number generation function
for the unit-Half-Normal-X distribution reparametrized in terms of the \tau
-th quantile, \tau \in (0, 1)
.
dughnx(x, mu, theta, tau = 0.5, log = FALSE)
pughnx(q, mu, theta, tau = 0.5, lower.tail = TRUE, log.p = FALSE)
qughnx(p, mu, theta, tau = 0.5, lower.tail = TRUE, log.p = FALSE)
rughnx(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(1-y\right) }\left( {\frac{y}{\alpha \left( 1-y\right) }}\right) ^{\theta }\mathrm{\exp }\left\{ -\frac{1}{2}\left[ {\frac{y}{\alpha \left( 1-y\right) }}\right] ^{2\theta }\right\}
Cumulative density function
F(y\mid \alpha ,\theta )=2\Phi \left[ \left( \frac{y}{\alpha \left(1-y\right) }\right) ^{\theta }\right] -1
Quantile Function
Q(\tau \mid \alpha )=\frac{\alpha \left[ \Phi ^{-1}\left( \frac{\tau +1}{2}\right) \right] ^{\frac{1}{\theta }}}{1+\alpha \left[ \Phi ^{-1}\left( \frac{ \tau +1}{2}\right) \right] ^{\frac{1}{\theta }}}
Reparametrization
\alpha=g^{-1}(\mu )=\frac{\mu }{\left( 1-\mu \right) \left[ \Phi ^{-1}\left( \frac{\tau +1}{2}\right) \right] ^{\frac{1}{\theta }}}
dughnx
gives the density, pughnx
gives the distribution function,
qughnx
gives the quantile function and rughnx
generates random deviates.
Invalid arguments will return an error message.
Josmar Mazucheli jmazucheli@gmail.com
André F. B. Menezes andrefelipemaringa@gmail.com
Bakouch, H. S., Nik, A. S., Asgharzadeh, A. and Salinas, H. S., (2021). A flexible probability model for proportion data: Unit-Half-Normal distribution. Communications in Statistics: CaseStudies, Data Analysis and Applications, 0(0), 1–18.
set.seed(123)
x <- rughnx(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-X')
lines(S, dughnx(x = S, mu = 0.5, theta = 2, tau = 0.5), col = 2)
plot(ecdf(x))
lines(S, pughnx(q = S, mu = 0.5, theta = 2, tau = 0.5), col = 2)
plot(quantile(x, probs = S), type = "l")
lines(qughnx(p = S, mu = 0.5, theta = 2, tau = 0.5), col = 2)
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