logistic5_fn {drda}  R Documentation 
5parameter logistic function
Description
Evaluate at a particular set of parameters the 5parameter logistic function.
Usage
logistic5_fn(x, theta)
Arguments
x 
numeric vector at which the logistic function is to be evaluated. 
theta 
numeric vector with the five parameters in the form

Details
The 5parameter logistic function f(x; theta)
is defined here as
g(x; theta) = 1 / (1 + nu * exp(eta * (x  phi)))^(1 / nu)
f(x; theta) = alpha + delta g(x; theta)
where theta = c(alpha, delta, eta, phi, nu)
, eta > 0
, and nu > 0
.
When delta
is positive (negative) the curve is monotonically increasing
(decreasing). When x > Inf
the value of the function is alpha
while the
value of the function for x > Inf
is alpha + delta
.
Parameter alpha
is the value of the function when x > Inf
.
Parameter delta
is the (signed) height of the curve.
Parameter eta
represents the steepness (growth rate) of the curve.
Parameter phi
is related to the midvalue of the function.
Parameter nu
affects near which asymptote maximum growth occurs.
Value
Numeric vector of the same length of x
with the values of the
logistic function.