# LLOGIS3: Three-Parameter Log-Logistic Distribution In FAdist: Distributions that are Sometimes Used in Hydrology

## Description

Density, distribution function, quantile function and random generation for the 3-parameter log-logistic distribution with shape, scale, and threshold (or shift) parameters equal to `shape`, `scale`, and `thres`, respectively.

## Usage

 ```1 2 3 4``` ```dllog3(x,shape=1,scale=1,thres=0,log=FALSE) pllog3(q,shape=1,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE) qllog3(p,shape=1,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE) rllog3(n,shape=1,scale=1,thres=0) ```

## Arguments

 `x,q` vector of quantiles. `p` vector of probabilities. `n` number of observations. `shape` shape parameter. `scale` scale parameter. `thres` threshold (or shift) parameter. `log,log.p` logical; if TRUE, probabilities p are given as log(p). `lower.tail` logical; if TRUE (default), probabilities are P[X <= x],otherwise, P[X > x].

## Details

If Y is a random variable distributed according to a logistic distribution (with location and scale parameters), then X = exp(Y)+m has a 3-parameter log-logistic distribution with shape and scale parameters corresponding to the scale and location parameteres of Y, respectively; and threshold parameter m.

## Value

`dllog3` gives the density, `pllog3` gives the distribution function, `qllog3` gives the quantile function, and `rllog3` generates random deviates.

`dlogis`, `plogis`, `qlogis`, `rlogis`, `dllog`, `pllog`, `qllog`, `rllog`

## Examples

 ```1 2 3 4 5``` ```m <- 100 x <- rllog3(10,1,0,m) dllog3(x,1,0,m) dllog(x-m,1,0) dlogis(log(x-m),0,1)/(x-m) ```

### Example output

```  0.04342902 0.02201302 0.78328575 0.30414739 0.32705660 0.17360111
 0.09856586 0.14587520 0.09103393 0.34519033
 0.04342902 0.02201302 0.78328575 0.30414739 0.32705660 0.17360111
 0.09856586 0.14587520 0.09103393 0.34519033
 0.04342902 0.02201302 0.78328575 0.30414739 0.32705660 0.17360111
 0.09856586 0.14587520 0.09103393 0.34519033
```

FAdist documentation built on April 17, 2020, 1:24 a.m.