ReversalGumbel {powdist} | R Documentation |
The Reversal-Gumbel Distribution
Description
Density, distribution function, quantile function and random generation for the Reversal-Gumbel distribution with parameters mu and sigma.
Usage
drgumbel(x, mu = 0, sigma = 1, log = FALSE)
prgumbel(q, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)
qrgumbel(p, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)
rrgumbel(n, mu = 0, sigma = 1)
Arguments
x , q |
vector of quantiles. |
mu , sigma |
location and scale parameters. |
log , log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are |
p |
vector of probabilities. |
n |
number of observations. |
Details
The reversal-Gumbel distribution has density
f(x)=\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 and \sigma^2>0
is the scale parameter.
References
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 São Paulo - Universidade Federal de São Carlos. Available in https://repositorio.ufscar.br/handle/ufscar/9016.
Bazán, J. L., Torres -Avilés, 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.
Examples
drgumbel(1, 3, 4)
prgumbel(1, 3, 4)
qrgumbel(0.2, 3, 4)
rprgumbel(5, 3, 4)