loglogistic6_fn {drda}  R Documentation 
6parameter loglogistic function
Description
Evaluate at a particular set of parameters the 6parameter loglogistic function.
Usage
loglogistic6_fn(x, theta)
Arguments
x 
numeric vector at which the function is to be evaluated. 
theta 
numeric vector with the six parameters in the form

Details
The 6parameter loglogistic function f(x; theta)
is defined here as
g(x; theta) = (x^eta / (xi * 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, xi)
, eta > 0
,
phi > 0
, nu > 0
, and xi > 0
. When delta
is positive (negative) the
curve is monotonically increasing (decreasing).
Parameter alpha
is the value of the function when x = 0
.
Parameter delta
affects the value of the function when x > Inf
.
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.
Parameter xi
affects the value of the function when x > Inf
.
Note: The 6parameter loglogistic function is overparameterized and nonidentifiable from data. It is available only for theoretical research.
Value
Numeric vector of the same length of x
with the values of the
loglogistic function.