Computes a value based on a linear growth curve reaching a plateau for time.
Usage
fn_linear_sat(t, t1 = 45, t2 = 80, k = 0.9)
Arguments
- t
Numeric. The time value.
- t1
Numeric. The lower threshold time. Default is 45.
- t2
Numeric. The upper threshold time. Default is 80.
- k
Numeric. The maximum value of the function. Default is 0.9. Assumed to be known.
Value
A numeric value based on the threshold model.
If t is less than t1, the function returns 0.
If t is between t1 and t2 (inclusive),
the function returns a value between 0 and k in a linear trend.
If t is greater than t2, the function returns k.
Details
$$
f(t; t_1, t_2, k) =
\begin{cases}
0 & \text{if } t < t_1 \\
\dfrac{k}{t_2 - t_1} \cdot (t - t_1) & \text{if } t_1 \leq t \leq t_2 \\
k & \text{if } t > t_2
\end{cases}
$$
Examples
library(flexFitR)
plot_fn(
fn = "fn_linear_sat",
params = c(t1 = 34.9, t2 = 61.8, k = 100),
interval = c(0, 108),
n_points = 2000,
auc_label_size = 3
)
