# W3: The three-parameter Weibull functions In drc: Analysis of Dose-Response Curves

## Description

'W1.3' and `W2.3` provide the three-parameter Weibull function, self starter function and names of the parameters.

'W1.3u' and 'W2.3u' provide three-parameter Weibull function where the upper limit is equal to 1, mainly for use with binomial/quantal response.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ``` W1.3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...) W2.3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...) W2x.3(fixed = c(NA, NA, NA), names = c("d", "e", "t0"), ...) W1.3u(upper = 1, fixed = c(NA, NA, NA), names = c("b", "c", "e"), ...) W2.3u(upper = 1, fixed = c(NA, NA, NA), names = c("b", "c", "e"), ...) ```

## Arguments

 `upper` numeric value. The fixed, upper limit in the model. Default is 1. `fixed` numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. `names` a vector of character strings giving the names of the parameters. The default is reasonable. `...` additional arguments to be passed from the convenience functions.

## Details

The three-parameter Weibull model is given by the expression

f(x) = 0 + (d-0)\exp(-\exp(b(\log(x)-e))).

The function is asymmetric about the inflection point, that is the parameter \exp(e).

The three-parameter Weibull model with upper limit 1 is given by the expression

f(x) = 0 + (1-0)\exp(-\exp(b(\log(x)-e))).

## Value

See `weibull1`.

## Note

This function is for use with the function `drm`.

## Author(s)

Christian Ritz

Related functions are `W1.4` and `weibull1`.
 ```1 2 3``` ```## Fitting a three-parameter Weibull model ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = W1.3()) ryegrass.m1 ```