# 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

 ```1 2 3 4``` ```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 [email protected]

## 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.

`llogisMLE`, `Lognormal`, `hllogis`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ```## 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) ```