Density, distribution function, quantile function and random generation for the power Reversal-Gumbel distribution with parameters mu, sigma and lambda.
dprgumbel(x, lambda = 1, mu = 0, sigma = 1, log = FALSE)pprgumbel(q, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE,
log.p = FALSE)
qprgumbel(p, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE,
log.p = FALSE)
rprgumbel(n, lambda = 1, mu = 0, sigma = 1)
vector of quantiles.
shape parameter.
location and scale parameters.
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are \(P[X \le x ]\), otherwise, P[X > x].
vector of probabilities.
number of observations.
The power reverlsa-Gumbel distribution has density
\(f(x)=\lambda \left[1-e^{-e^{\left(\frac{x-\mu}{\sigma}\right)}}\right]^{\lambda-1}\left[\frac{1}{\sigma}e^{\left(\frac{x-\mu}{\sigma}\right)-e^{\left(\frac{x-\mu}{\sigma}\right)}} \right]\),
where \(-\infty<\mu<\infty\) is the location paramether, \(\sigma^2>0\) the scale parameter and \(\lambda>0\) the shape parameter.
Abanto -Valle, C. A., Baz<U+00E1>n, J. L. and Smith, A. C. (2014) State space mixed models for binary responses with skewed inverse links using JAGS. Rio de Janeiro, Brazil.
Anyosa, S. A. C. (2017) Binary regression using power and reversal power links. Master's thesis in Portuguese. Interinstitutional Graduate Program in Statistics. Universidade de S<U+00E3>o Paulo - Universidade Federal de S<U+00E3>o Carlos. Available in https://repositorio.ufscar.br/handle/ufscar/9016.
Baz<U+00E1>n, J. L., Torres -Avil<U+00E9>s, F., Suzuki, A. K. and Louzada, F. (2017) Power and reversal power links for binary regressions: An application for motor insurance policyholders. Applied Stochastic Models in Business and Industry, 33(1), 22-34.
# NOT RUN {
dprgumbel(1, 1, 3, 4)
pprgumbel(1, 1, 3, 4)
qprgumbel(0.2, 1, 3, 4)
rprgumbel(5, 2, 3, 4)
# }
Run the code above in your browser using DataLab