llogistic: The L-Logistic Distribution

In llogistic: 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[X ≤q x ], otherwise, P[X > x].
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)

Example output

[1] 1.248514
[1] 0.8448276
[1] 0.3333333
 [1] 0.4334053 0.6585362 0.6795353 0.4428677 0.4749751 0.4466718 0.7992647
 [8] 0.4643332 0.6531001 0.1111268

llogistic documentation built on May 2, 2019, 6:52 a.m.