logistic6_fn {drda}R Documentation

6-parameter logistic function


Evaluate at a particular set of parameters the 6-parameter logistic function.


logistic6_fn(x, theta)



numeric vector at which the function is to be evaluated.


numeric vector with the six parameters in the form c(alpha, delta, eta, phi, nu, xi).


The 6-parameter logistic function ⁠f(x; theta)⁠ is defined here as

⁠g(x; theta) = 1 / (xi + nu * exp(-eta * (x - phi)))^(1 / nu)⁠ ⁠f(x; theta) = alpha + delta g(x; theta)⁠

where theta = c(alpha, delta, eta, phi, nu, xi), eta > 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 -> -Inf. 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 mid-value 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 6-parameter logistic function is over-parameterized and non-identifiable from data. It is available only for theoretical research.


Numeric vector of the same length of x with the values of the logistic function.

[Package drda version 2.0.3 Index]