meW: Four-parameter Weibull functions

In DoseResponse/medrc: Mixed effect dose-response curves

Description

'W1.X' and 'W2.X' provide the X-parameter Weibull functions.

Usage

meW1.2(x, b, e)

meW1.3(x, b, d, e)

meW1.4(x, b, c, d, e)

meW2.2(x, b, e)

meW2.3(x, b, d, e)

meW2.4(x, b, c, d, e)

Arguments

x	numeric dose vector.
b	steepness
e	ED50
d	upper limit
c	lower limit

Details

As pointed out in Seber and Wild (1989), there exist two different parameterisations of the Weibull model. They do not yield the same fitted curve for a given dataset. The four-parameter Weibull type 1 model ('weibull1') is

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

Thw four-parameter Weibull type 2 model ('weibull2') is

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

Both four-parameter model functions are asymmetric with inflection point at the dose equal e.

References

Seber, G. A. F. and Wild, C. J (1989) Nonlinear Regression, New York: Wiley \& Sons (pp. 330–331). Ritz, C (2009) Towards a unified approach to dose-response modeling in ecotoxicology To appear in Environ Toxicol Chem.

DoseResponse/medrc documentation built on May 28, 2019, 12:36 p.m.