ReversalPowerNormal {powdist}

The Reversal Power Normal Distribution

Description

Density, distribution function, quantile function and random generation for the reversal power normal distribution with parameters mu, sigma and lambda.

Usage

drpnorm(x, lambda = 1, mu = 0, sigma = 1, log = FALSE)

prpnorm(q, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE,
  log.p = FALSE)

qrpnorm(p, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE,
  log.p = FALSE)

rrpnorm(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 reversal power Normal distribution has density

f(x)=\lambda \left [ \Phi \left ( -\frac{x-\mu}{\sigma} \right ) \right ]^{\lambda - 1} \left[\frac{e^{ -\frac{1}{2}\left ( \frac{x-\mu}{\sigma} \right )^2}}{\sigma\sqrt{2\pi}} \right],

where -\infty<\mu<\infty is the location paramether, \sigma^2>0 the scale parameter and \lambda>0 the shape 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.

Bazán, J. L., Romeo, J. S. and Rodrigues, J. (2014) Bayesian skew-probit regression for binary response data. Brazilian Journal of Probability and Statistics. 28(4), 467–482.

Examples

drpnorm(1, 1, 3, 4)
prpnorm(1, 1, 3, 4)
qrpnorm(0.2, 1, 3, 4)
rrpnorm(5, 2, 3, 4)