flexFitR (version 1.2.2)

fn_logistic: Logistic function

Description

A standard logistic function commonly used to model sigmoidal growth. The curve rises from near zero to a maximum value k, with inflection point at t0 and growth rate a.

Usage

fn_logistic(t, a, t0, k)

Value

A numeric vector of the same length as t, representing the logistic function values.

Arguments

t

A numeric vector of input values (e.g., time).

a

The growth rate (steepness of the curve). Higher values lead to a steeper rise.

t0

The time of the inflection point (midpoint of the transition).

k

The upper asymptote or plateau (maximum value as t -> Inf).

Details

$$ f(t; a, t0, k) = \frac{k}{1 + e^{-a(t - t_0)}} $$

This is a classic sigmoid (S-shaped) curve that is symmetric around the inflection point t0.

Examples

library(flexFitR)
plot_fn(
  fn = "fn_logistic",
  params = c(a = 0.199, t0 = 47.7, k = 100),
  interval = c(0, 108),
  n_points = 2000
)