using the exgaus distribution to model response time

media_mix_modeling_exGAUS.R

# https://link.springer.com/article/10.1057/jma.2014.3#Tab2
# using the exgaus distribution to model response time

library(tidyverse)
data.frame(x=c(0, 20)) %>% 
ggplot(aes(x)) + 
  stat_function(fun=function(x) dexGAUS(x, mu=1, sigma=2, nu=3),
                linetype = 1) +
  stat_function(fun=function(x) dexGAUS(x, mu=4, sigma=0.04, nu=4),
                linetype = 2) +
  stat_function(fun=function(x) dexGAUS(x, mu=8, sigma=1, nu=0.5),
                linetype = 3) +
  theme_classic()

using the normalized lower incomplete gamma

library(tidyverse)
data.frame(x=c(0, 10)) %>% 
ggplot(aes(x)) + 
  stat_function(fun=function(x) pgamma(x, shape = 4, rate = 1),
                linetype = 1, size = 1) +
    stat_function(fun=function(x) pgamma(x, shape = 2, rate = 1/.8),
                linetype = 2, size = 1) +
    stat_function(fun=function(x) pgamma(x, shape = .5, rate = 1/4),
                linetype = 3, size = 1) +
theme_classic()