Exercice1_Luk

# ex 1 risk and uncertainty
library(ggplot2)
library(dplyr)



# define concentration function
calc_con = function(O1,O2,O3, t){
  C <- O1/((t/O2+1)^O3)
  C
}

## do each step for uniform distribution and normal distribution

# create input data with uniform distributed uncertainties
sim_unif = data.frame(t = rep(c(1:100),10000),
                 O1 = runif(10000*100,80,90),
                 O2 = runif(10000*100,1,3),
                 O3 = runif(10000*100,0.5,1.5))

# create input data with non uniform distributed uncertainties
sim_norm = data.frame(t = rep(c(1:100),10000),
                 O1 = rnorm(10000*100,85,2.4),
                 O2 = runif(10000*100,1,3),
                 O3 = runif(10000*100,0.5,1.5))



# calculate concentration on input data
sim_unif$con = calc_con(sim_unif$O1, sim_unif$O2, sim_unif$O3, sim_unif$t)
sim_norm$con = calc_con(sim_norm$O1, sim_norm$O2, sim_norm$O3, sim_norm$t)

# calculate the mean and the lower and upper confidence intervall
df_plot_unif = sim_unif %>%
              group_by(t) %>%
                          do(data.frame(mean = mean(.$con),
                                        lower = quantile(.$con, c(.025)),
                                        upper = quantile(.$con, c(.975))
                                        )
                            )

df_plot_norm = sim_norm %>%
  group_by(t) %>%
  do(data.frame(mean = mean(.$con),
                lower = quantile(.$con, c(.025)),
                upper = quantile(.$con, c(.975))
  )
  )



# plot result
ggplot()+
  geom_line(data = df_plot_unif, aes(x = t, y = mean))+
  geom_ribbon(data = df_plot_unif, aes(x = t, ymin = lower, ymax = upper, alpha = 0.5, fill = "unif"))+
  geom_line(data = df_plot_norm, aes(x = t, y = mean))+
  geom_ribbon(data = df_plot_norm, aes(x = t, ymin = lower, ymax = upper, alpha = 0.5, fill = "norm"))+
  ylab(label = "concentration")