ReversalPowerNormal: The Reversal Power Normal Distribution

In susanca/powdist: Power and Reversal Power Distributions

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 ≤ x ], otherwise, P[X > x].
p	vector of probabilities.
n	number of observations.

Details

The reversal power Normal distribution has density

f(x)=[λ/σ][exp(-((x-μ)/σ)^2)/√(2π)][Φ(-(x-μ)/σ)]^(λ-1),

where -∞<μ<∞ is the location paramether, σ^2>0 the scale parameter and λ>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<c3><a3>o Paulo - Universidade Federal de S<c3><a3>o Carlos. Available in https://repositorio.ufscar.br/handle/ufscar/9016.

Baz<c3><a1>n, J. L., Torres -Avil<c3><a9>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<c3><a1>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<e2><80><93>482.

Examples

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

susanca/powdist documentation built on May 24, 2019, 7:20 a.m.