if (!require(quantmod)) install.packages('quantmod')
if (!require(moments)) install.packages('moments')

library(quantmod)
library(moments)

##### Exemple - Variable discrète #####

set.seed(123) # Afin d'assurer la reproductivité du résultat 
random_numbers <- sample(1:6, 1000, replace = TRUE)
hist(random_numbers, 
     breaks = seq(0.5, 6.5, by = 1), 
     main = "Histogramme des résultats de 1 000 lancements de dé",
     xlab = "Résultat",
     ylab = "Fréquence")


##### Exemple - Variable continue #####

CAC40 <- getSymbols("^FCHI", from = "2021-04-01", to   = "2023-04-01", env = NULL) 
CAC40 <- CAC40[!is.na(CAC40[,6]),] #enlever les jours de valeurs NA (le cas échéant)

# Compute logarithmic percentage returns (with respect to the daily closing prices)
CAC40$return = diff(log(CAC40[,6]))*100

# Convert the xts object (from the QuantMod R package) to a data frame and process dates 
CAC40 <- data.frame(Date=index(CAC40), coredata(CAC40))
CAC40$Date <- as.POSIXct(CAC40$Date)

CAC40 <- CAC40[-1,]

my_breaks <- seq(-10, 10, by = 0.5)
hist(CAC40$return, freq = FALSE, breaks = my_breaks, main = "Distribution des rendements journaliers de CAC-40")
dens <- density(CAC40$return)
curve(dnorm(x, mean(CAC40$return), sd(CAC40$return)), add = TRUE, col = "red", 
          lwd = 1, lty=2)
legend("topright", legend = c("Estimation de la distribution", "Distribution normale"), col = c("blue", "red"), lwd = 1, cex =0.8,lty=2)

# Calcul des statistiques descriptives
mean(CAC40$return)
median(CAC40$return)
sd(CAC40$return)
skewness(CAC40$return)
kurtosis(CAC40$return)