Computes a value based on an exponential growth curve and exponential decay model for time.
Usage
fn_exp2_exp(t, t1, t2, alpha, beta)
Arguments
- t
Numeric. The time value.
- t1
Numeric. The lower threshold time. Assumed to be known.
- t2
Numeric. The upper threshold time.
- alpha
Numeric. The parameter for the first exponential term.
Must be greater than 0.
- beta
Numeric. The parameter for the second exponential term.
Must be less than 0.
Value
A numeric value based on the double exponential model.
If t is less than t1, the function returns 0.
If t is between t1 and t2 (inclusive),
the function returns exp(alpha * (t - t1)^2) - 1.
If t is greater than t2, the function returns
(exp(alpha * (t2 - t1)^2) - 1) * exp(beta * (t - t2)).
Details
$$
f(t; t_1, t_2, \alpha, \beta) =
\begin{cases}
0 & \text{if } t < t_1 \\
e^{\alpha \cdot (t - t_1)^2} - 1 & \text{if } t_1 \leq t \leq t_2 \\
\left(e^{\alpha \cdot (t_2 - t_1)^2} - 1\right) \cdot e^{\beta \cdot (t - t_2)} & \text{if } t > t_2
\end{cases}
$$
Examples
library(flexFitR)
plot_fn(
fn = "fn_exp2_exp",
params = c(t1 = 35, t2 = 55, alpha = 1 / 600, beta = -1 / 30),
interval = c(0, 108),
n_points = 2000,
auc_label_size = 3,
y_auc_label = 0.15
)
