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drda (version 2.0.5)

loglogistic5_fn: 5-parameter log-logistic function

Description

Evaluate at a particular set of parameters the 5-parameter log-logistic function.

Usage

loglogistic5_fn(x, theta)

Value

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

Arguments

x

numeric vector at which the function is to be evaluated.

theta

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

Details

The 5-parameter log-logistic 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 mid-value of the function. Parameter nu affects near which asymptote maximum growth occurs.