W3 function

The three-parameter Weibull functions

'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.

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

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

Returns

See weibull1.

Author(s)

Christian Ritz

Note

This function is for use with the function drm.

See Also

Related functions are W1.4 and weibull1.

Examples

## Fitting a three-parameter Weibull model
ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = W1.3())
ryegrass.m1