Evaluate at a particular set of parameters the gradient and Hessian of the 2-parameter logistic function.
logistic2_gradient(x, theta, delta)logistic2_hessian(x, theta, delta)
logistic2_gradient_hessian(x, theta, delta)
Gradient or Hessian evaluated at the specified point.
numeric vector at which the function is to be evaluated.
numeric vector with the two parameters in the form
c(eta, phi).
value of delta parameter (either 1 or -1).
The 2-parameter 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) and eta > 0. Only eta and phi
are free to vary (therefore the name) while vector c(alpha, delta) is
constrained to be either c(0, 1) (monotonically increasing curve) or
c(1, -1) (monotonically decreasing curve).