ReversalPowerLogistic: The Reversal Power Logistic Distribution

In powdist: Power and Reversal Power Distributions

Description

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

Usage

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

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

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

rrplogis(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 Logistic distribution has density

f(x)=[λ/σ][exp(-(x-μ)/σ)/(1+exp(-(x-μ)/σ))^2][exp(-(x-μ)/σ)/(1+exp(-(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 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.

Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 16. Wiley, New York.

Nagler J. (1994) Scobit: an alternative estimator to logit and probit. American Journal Political Science, 38(1), 230-255.

Prentice, R. L. (1976) A Generalization of the probit and logit methods for dose-response curves. Biometrika, 32, 761-768.

Examples

drplogis(1, 1, 3, 4)
prplogis(1, 1, 3, 4)
qrplogis(0.2, 1, 3, 4)
rrplogis(5, 2, 3, 4)

powdist documentation built on May 1, 2019, 10:11 p.m.