fn_lin_logis {flexFitR} | R Documentation |
Linear-logistic function
Description
A piecewise function that models an initial linear increase followed by a logistic saturation.
Usage
fn_lin_logis(t, t1, t2, k)
Arguments
t |
A numeric vector of input values (e.g., time). |
t1 |
The onset time of the response. The function is 0 for all values less than |
t2 |
The transition time between the linear and logistic phases. Must be greater than |
k |
The plateau height. The function transitions toward this value in the logistic phase. |
Details
f(t; t_1, t_2, k) =
\begin{cases}
0 & \text{if } t < t_1 \\
\dfrac{k}{2(t_2 - t_1)} \cdot (t - t_1) & \text{if } t_1 \leq t \leq t_2 \\
\dfrac{k}{1 + e^{-2(t - t_2) / (t_2 - t_1)}} & \text{if } t > t_2
\end{cases}
The linear segment rises from 0 starting at t1
, and the logistic segment begins at t2
,
smoothly approaching the plateau value k
.
Value
A numeric vector of the same length as t
, representing the function values.
Examples
library(flexFitR)
plot_fn(
fn = "fn_lin_logis",
params = c(t1 = 35, t2 = 50, k = 100),
interval = c(0, 108),
n_points = 2000,
auc_label_size = 3
)