df1 = data.frame(normal_sim[61,])
df3 = data.frame(snormal_sim09[61,])
df4 = data.frame(t_sim2.1[61,])
df7 = data.frame(st_sim2.1_09[61,])

ggplot() +
geom_density(data = df7, aes(x = st_sim2.1_09[61,]),colour = 'pink',
               size = 1.1,show.legend = F) +
coord_cartesian(xlim = c(-4.5, 4.5)) +
  labs( x = expression(y[r]), y=expression("Densities"))+
  theme_bw()

ggplot() +
  stat_function(data = data.frame(x = c(-3, 3)), aes(x),colour = 'yellow',fun = dnorm,n=100000 ,args = list(mean = 0, sd = 1), size=1.1) +
  geom_density(data = df3, aes(x =snormal_sim09[61,]),colour = 'blue',
               size = 1.1,show.legend = F) +
  geom_density(data = df4, aes(x = t_sim2.1[61,]),colour = 'green',
               size = 1.1,show.legend = F) +
  geom_density(data = df7, aes(x = st_sim2.1_09[61,]),colour = 'pink',
               size = 1.1,show.legend = F) +
  geom_density(data = df1, aes(x = normal_sim[61,]),colour = 'black',
               size = 1.1,show.legend = FALSE)+
  coord_cartesian(xlim = c(-4.5, 4.5)) +
  labs( x = expression(y[r]), y=expression("Densities"))+
  theme_bw()