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

1 2 3 4 |

`x, q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`n` |
number of observations. If |

`location, scale` |
location and scale parameters (non-negative numeric). |

`lower.tail` |
logical; if |

`log, log.p` |
logical; if |

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.*

`dllogis`

gives the density, `pllogis`

gives the
distribution function, `qllogis`

gives the quantile function
and `rllogis`

generates random deviates.

Christophe Pouzat christophe.pouzat@gmail.com

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)
``` |

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