Description Usage Arguments Details Value References Examples
Density, distribution function, quantile function and random
generation for the logistic distribution with parameters
location
and scale
.
1 2 3 4 5  dglogis(x, location = 0, scale = 1, shape = 1, log = FALSE)
pglogis(q, location = 0, scale = 1, shape = 1, lower.tail = TRUE, log.p = FALSE)
qglogis(p, location = 0, scale = 1, shape = 1, lower.tail = TRUE, log.p = FALSE)
rglogis(n, location = 0, scale = 1, shape = 1)
sglogis(x, location = 0, scale = 1, shape = 1)

x, q 
vector of quantiles. 
p 
vector of probabilities. 
n 
number of observations. If 
location, scale, shape 
location, scale, and shape parameters (see below). 
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]. 
If location
, scale
, or shape
are omitted, they assume the
default values of 0
, 1
, and 1
, respectively.
The generalized logistic distribution with location
= m,
scale
= s, and shape
= g has distribution function
F(x) = 1 / (1 + exp((xm)/s))^g
.
The mean is given by location + (digamma(shape)  digamma(1)) * scale
, the variance by
(psigamma(shape, deriv = 1) + psigamma(1, deriv = 1)) * scale^2)
and the skewness by
(psigamma(shape, deriv = 2)  psigamma(1, deriv = 2)) / (psigamma(shape, deriv = 1) + psigamma(1, deriv = 1))^(3/2))
.
[dpq]glogis
are calculated by leveraging the [dpq]logis
and adding the shape parameter. rglogis
uses inversion.
dglogis
gives the probability density function,
pglogis
gives the cumulative distribution function,
qglogis
gives the quantile function, and
rglogis
generates random deviates.
sglogis
gives the score function (gradient of the logdensity with
respect to the parameter vector).
Johnson NL, Kotz S, Balakrishnan N (1995) Continuous Univariate Distributions, volume 2. John Wiley \& Sons, New York.
Shao Q (2002). Maximum Likelihood Estimation for Generalised Logistic Distributions. Communications in Statistics – Theory and Methods, 31(10), 1687–1700.
Windberger T, Zeileis A (2014). Structural Breaks in Inflation Dynamics within the European Monetary Union. Eastern European Economics, 52(3), 66–88.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  ## PDF and CDF
par(mfrow = c(1, 2))
x < 100:100/10
plot(x, dglogis(x, shape = 2), type = "l", col = 4, main = "PDF", ylab = "f(x)")
lines(x, dglogis(x, shape = 1))
lines(x, dglogis(x, shape = 0.5), col = 2)
legend("topleft", c("generalized (0, 1, 2)", "standard (0, 1, 1)",
"generalized (0, 1, 0.5)"), lty = 1, col = c(4, 1, 2), bty = "n")
plot(x, pglogis(x, shape = 2), type = "l", col = 4, main = "CDF", ylab = "F(x)")
lines(x, pglogis(x, shape = 1))
lines(x, pglogis(x, shape = 0.5), col = 2)
## artifical empirical example
set.seed(2)
x < rglogis(1000, 1, scale = 0.5, shape = 3)
gf < glogisfit(x)
plot(gf)
summary(gf)

Loading required package: zoo
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
Call:
glogisfit(x = x)
Coefficients:
Estimate Std. Error z value Pr(>z)
location 1.16961 0.18840 6.208 5.36e10 ***
log(scale) 0.63017 0.04323 14.578 < 2e16 ***
log(shape) 1.29581 0.25916 5.000 5.73e07 ***

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Loglikelihood: 1074 on 12 Df
Goodnessoffit statistic: 39.11 on 58 DF, pvalue: 0.9731
Number of iterations in BFGS optimization: 15
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