loglogistic5_fn {drda}  R Documentation 
5parameter loglogistic function
Description
Evaluate at a particular set of parameters the 5parameter loglogistic function.
Usage
loglogistic5_fn(x, theta)
Arguments
x 
numeric vector at which the function is to be evaluated. 
theta 
numeric vector with the five parameters in the form

Details
The 5parameter loglogistic function f(x; theta)
is defined here as
g(x; theta) = (x^eta / (x^eta + nu * phi^eta))^(1 / nu)
f(x; theta) = alpha + delta g(x; theta)
where x >= 0
, theta = c(alpha, delta, eta, phi, nu)
, eta > 0
,
phi > 0
, and nu > 0
.
Parameter alpha
is the value of the function when x = 0
.
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
loglogistic function.