PowerLogistic: The Power Logistic Distribution

Description Usage Arguments Details References Examples

Description

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

Usage

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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 ≤ x ], otherwise, P[X > x].

p

vector of probabilities.

n

number of observations.

Details

The 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.

Lemonte, A. J. and Bazán, 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

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dplogis(1, 1, 3, 4)
pplogis(1, 1, 3, 4)
qplogis(0.2, 1, 3, 4)
rplogis(5, 2, 3, 4)

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