PowerReversalGumbel {powdist}

The Power Reversal-Gumbel Distribution

Description

Density, distribution function, quantile function and random generation for the power Reversal-Gumbel distribution with parameters mu, sigma and lambda.

Usage

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)

Arguments

x, q

vector of quantiles.

lambda

shape parameter.

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[X \le x ], otherwise, P[X > x].

p

vector of probabilities.

n

number of observations.

Details

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.

References

Abanto -Valle, C. A., Bazán, 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 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

dprgumbel(1, 1, 3, 4)
pprgumbel(1, 1, 3, 4)
qprgumbel(0.2, 1, 3, 4)
rprgumbel(5, 2, 3, 4)