dllogis: The Log Logistic Distribution

In STAR: Spike Train Analysis with R

Description

Density, distribution function, quantile function, and random generation for the log logistic.

Usage

dllogis(x, location = 0, scale = 1, log = FALSE)
pllogis(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
qllogis(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
rllogis(n, location = 0, scale = 1)

Arguments

x, q	vector of quantiles.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.
location, scale	location and scale parameters (non-negative numeric).
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
log, log.p	logical; if TRUE, probabilities p are given as log(p).

Details

If location or scale are omitted, they assume the default values of 0 and 1 respectively.

The log-Logistic distribution with location = m and scale = s has distribution function

F(x) = 1 / (1 + exp(-(log(x)-m)/s))

and density

f(x) = 1/(s*x) exp(-(log(x)-m)/s) (1 + exp(-(log(x)-m)/s))^-2.

Value

dllogis gives the density, pllogis gives the distribution function, qllogis gives the quantile function and rllogis generates random deviates.

Author(s)

Christophe Pouzat [e-mail]

References

Lindsey, J.K. (2004) Introduction to Applied Statistics: A Modelling Approach. OUP.

Lindsey, J.K. (2004) The Statistical Analysis of Stochastic Processes in Time. CUP.

See Also

llogisMLE, Lognormal, hllogis

Examples

## Not run: 
tSeq <- seq(0.001,0.6,0.001)
location.true <- -2.7
scale.true <- 0.025
Yd <- dllogis(tSeq, location.true, scale.true)
Yh <- hllogis(tSeq, location.true, scale.true)
max.Yd <- max(Yd)
max.Yh <- max(Yh)
Yd <- Yd / max.Yd
Yh <- Yh / max.Yh
oldpar <- par(mar=c(5,4,4,4))
plot(tSeq, Yd, type="n", axes=FALSE, ann=FALSE,
     xlim=c(0,0.6), ylim=c(0,1))
axis(2,at=seq(0,1,0.2),labels=round(seq(0,1,0.2)*max.Yd,digits=2))
mtext("Density (1/s)", side=2, line=3)
axis(1,at=pretty(c(0,0.6)))
mtext("Time (s)", side=1, line=3)
axis(4, at=seq(0,1,0.2), labels=round(seq(0,1,0.2)*max.Yh,digits=2))
mtext("Hazard (1/s)", side=4, line=3, col=2)
mtext("Log Logistic Density and Hazard Functions", side=3, line=2,cex=1.5)
lines(tSeq,Yd)
lines(tSeq,Yh,col=2)
par(oldpar)

## End(Not run)

Example output

Loading required package: survival
Loading required package: mgcv
Loading required package: nlme
This is mgcv 1.8-28. For overview type 'help("mgcv-package")'.
Loading required package: R2HTML
Loading required package: gss
Loading required package: codetools

STAR documentation built on May 2, 2019, 11:44 a.m.