logistic4_fn {drda}  R Documentation 
4parameter logistic function
Description
Evaluate at a particular set of parameters the 4parameter logistic function.
Usage
logistic4_fn(x, theta)
Arguments
x 
numeric vector at which the logistic function is to be evaluated. 
theta 
numeric vector with the four parameters in the form

Details
The 4parameter logistic function f(x; theta)
is defined here as
g(x; theta) = 1 / (1 + exp(eta * (x  phi)))
f(x; theta) = alpha + delta g(x; theta)
where theta = c(alpha, delta, eta, phi)
, alpha
is the value of the
function when x > Inf
, delta
is the (signed) height of the curve,
eta > 0
is the steepness of the curve or growth rate (also known as the
Hill coefficient), and phi
is the value of x
at which the curve is equal
to its midpoint.
When delta < 0
the curve is monotonically decreasing while it is
monotonically increasing for delta > 0
.
The midpoint f(phi; theta)
is equal to alpha + delta / 2
while the value
of the function for x > Inf
is alpha + delta
.
Value
Numeric vector of the same length of x
with the values of the
logistic function.