conf (version 1.8.3)

dllogis: The Log Logistic Distribution

Description

Density, distribution function, quantile function, and random generation for the log logistic distribution. The corresponding code for these functions as well as the manual information included here is attributed to Christophe Pouzat's STAR Package (archived 2022-05-23).

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)

Value

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

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).

Author

Christophe Pouzat

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

$$\mathrm{F}(x) = \frac{1}{1+ \exp(-\frac{\log (x) - m}{s})}$$

and density

$$f(x)=\frac{1}{s \, x} \frac{\exp (-\frac{\log (x) - m}{s})}{(1+ \exp(-\frac{\log (x) - m}{s}))^2}$$.

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.

Examples

if (FALSE) {
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)
}