The log-logistic function

'meLL.X' provides the X-parameter log-logistic function.

meLL.2(x, b, e)

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

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

meLL.5(x, b, c, d, e, f)

Arguments

x

numeric dose vector.
b

steepness
e

ED50
d

upper limit
c

lower limit
f

asymmetry

Details

The five-parameter logistic function is given by the expression $$ f(x) = c + \frac{d-c}{(1+\exp(b(\log(x)-\log(e))))^f}$$ or in another parameterisation $$ f(x) = c + \frac{d-c}{(1+\exp(b(\log(x)-e)))^f}$$ The function is asymmetric for \(f\) different from 1.

References

Finney, D. J. (1979) Bioassay and the Practise of Statistical Inference, Int. Statist. Rev., 47, 1--12.