# drexp: The Refractory Exponential Distribution In STAR: Spike Train Analysis with R

## Description

Density, distribution function, quantile function, and random generation for the refractory exponential.

## Usage

 ```1 2 3 4``` ```drexp(x, rate = 10, rp = 0.005, log = FALSE) prexp(q, rate = 10, rp = 0.005, lower.tail = TRUE, log.p = FALSE) qrexp(p, rate = 10, rp = 0.005, lower.tail = TRUE, log.p = FALSE) rrexp(n, rate = 10, rp = 0.005) ```

## 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. `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). `rate` rate parameter (non-negative numeric). `rp` refractory period parameter (non-negative numeric).

## Details

The refractory exponential distribution with `rate`, r, and ```refractory period```, rp, has density:

f(x) = r exp(- r (x-rp))

for `x >= rp`.

## Value

`drexp` gives the density, `prexp` gives the distribution function, `qrexp` gives the quantile function and `rrexp` generates random deviates.

## Author(s)

Christophe Pouzat [email protected]

## References

Johnson, D. H. and Swami, A. (1983) The transmission of signals by auditory-nerve fiber discharge patterns. J. Acoust. Soc. Am. 74: 493–501.

`rexpMLE`
 ``` 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) rate.true <- 20 rp.true <- 0.01 Yd <- drexp(tSeq, rate.true, rp.true) Yh <- hrexp(tSeq, rate.true, rp.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("Refractory Exponential Density and Hazard Functions", side=3, line=2,cex=1.5) lines(tSeq,Yd) lines(tSeq,Yh,col=2) par(oldpar) ## End(Not run) ```