powdist (version 0.1.4)

PowerLogistic: The Power Logistic Distribution

Description

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

Usage

dplogis(x, lambda = 1, mu = 0, sigma = 1, log = FALSE)
pplogis(q, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE,
  log.p = FALSE)
qplogis(p, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE,
  log.p = FALSE)
rplogis(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 Logistic distribution has density

$f(x)=\lambda {\left[\frac{1}{1+e^{-\left(\frac{x-\mu }{\sigma }\right)}}\right]}^{\lambda -1}\left[\frac{e^{-\left(\frac{x-\mu }{\sigma }\right)}}{\sigma {(1+e^{-\left(\frac{x-\mu }{\sigma }\right)})}^2}\right]$, where $-\mathrm{\infty }<\mu <\mathrm{\infty }$ 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.

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

Lemonte, A. J. and Baz<U+00E1>n, J. L. (2017) New links for binary regression: an application to coca cultivation in Peru. TEST.

Nadarajah, S. (2009) The skew logistic distribution. AStA Advances in Statistical Analysis, 93, 187-203.

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

Examples

# NOT RUN {
dplogis(1, 1, 3, 4)
pplogis(1, 1, 3, 4)
qplogis(0.2, 1, 3, 4)
rplogis(5, 2, 3, 4)
# }