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powdist (version 0.1.4)

ReversalPowerNormal: 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 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.

Baz<U+00E1>n, 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<U+2013>482.

Examples

Run this code
# NOT RUN {
drpnorm(1, 1, 3, 4)
prpnorm(1, 1, 3, 4)
qrpnorm(0.2, 1, 3, 4)
rrpnorm(5, 2, 3, 4)
# }

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