| Title: | The L-Logistic Distribution |
| Version: | 1.0.3 |
| Description: | Density, distribution function, quantile function and random generation for the L-Logistic distribution with parameters m and phi. The parameter m is the median of the distribution. |
| Imports: | stats |
| Depends: | R (≥ 3.3.0) |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 6.1.0 |
| NeedsCompilation: | no |
| Packaged: | 2019-03-31 19:47:13 UTC; Sara |
| Author: | Rosineide Fernando da Paz [aut, cre], Jorge Luís Bazán [ctb] |
| Maintainer: | Rosineide Fernando da Paz <rfpaz2@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2019-03-31 20:20:03 UTC |
The L-Logistic Distribution
Description
Density, distribution function, quantile function and random generation for the L-Logistic distribution with parameters m and phi.
Usage
dllogistic(x, m, phi, log = FALSE)
pllogistic(q, m, phi, lower.tail = TRUE, log.p = FALSE)
qllogistic(p, m, phi, lower.tail = TRUE, log.p = FALSE)
rllogistic(n, m, phi)
Arguments
x, q |
vector of quantiles. |
m, phi |
parameters of the L-Logistic distribution. The parameter m lies in the interval (0,1) and phi is positive. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are |
p |
vector of probabilities. |
n |
number of observations. |
Details
The llogistic distribution has density
f(x)=phi (1 - m)^phi m^phi (x(1 - x))^(phi - 1)/((1 - m)^phi x^phi + m^phi (1 - x)^phi)^2,
for 0< x < 1, where m is a median of the distribution and phi is a shape parameter.
Value
dllogistic(x,m,phi) gives the density function, rllogistic(n,m,phi) gives n random variates and qllogistic(p,m,phi) gives the quantile.
Source
The L-Losgistic distribution was introduced by Tadikamalla and Johnson (1982), which refer to this distribution as Logit-Logistic distribution. Here, we have a new parameterization of the Logit-Logistic with the median as a parameter.
References
Paz, R.F., Balakrishnan, N and Bazán, Jorge L. (2016). L-Logistic Distribution: Properties, Inference and an Application to Study Poverty and Inequality in Brazil. São Carlos: Universidade Federal de São Carlos. Tecnical-Scientific Report No. 261, Teory and Method. Sponsored by the Department of Statistical, <URL:http://www.pipges.ufscar.br/publicacoes/relatorios-tecnicos/arquivos-1/rt261.pdf>.
TADIKAMALLA, P. R.; JOHNSON, N. L. (1982). Systems of frequency curves generated by transformations of logistic variables. Biometrika, v. 69, n. 2, p. 461.
Examples
dllogistic(0.3, 0.5, 2)
pllogistic(0.7, 0.5, 2)
qllogistic(0.2, 0.5, 2)
rllogistic(10, 0.5, 2)