Linear plateau function — fn_linear

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

$f (t; t_{1}, t_{2}, k) = {\begin{cases} 0 & if t < t_{1} \\ \frac{k}{t_{2} - t_{1}} \cdot (t - t_{1}) & if t_{1} \leq t \leq t_{2} \\ k & if t > t_{2} \end{cases}$

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
)