Plotting the CDF and Quantile Functions Given the PDF - r

Question

How would I plot the CDF and Quantile functions, in R, if I have the PDF. Currently, I have the following (but I think there must be a better way to do it):
## Probability Density Function
p <- function(x) {
result <- (x^2)/9
result[x < 0 | x > 3] <- 0
result
}
plot(p, xlim = c(0,3), main="Probability Density Function")
## Cumulative Distribution Function
F <- function(a = 0,b){
result <- ((b^3)/27) - ((a^3)/27)
result[a < 0 ] <- 0
result[b > 3] <- 1
result
}
plot(F(,x), xlim=c(0,3), main="Cumulative Distribution Function")
## Quantile Function
Finv <- function(p) {
3*x^(1/3)
}

Answer 1

As #dash2 suggested, the CDF would need you to integrate the PDF, in essence needing you to find the area under the curve.
Here's a generic solution which should help. I am using a gaussian distribution as an example - you should be able to feed to it any generic function.
Note that quantiles reported are approximations only. Also, dont forget to look into the documentation for integrate().
# CDF Function
CDF <- function(FUNC = p, plot = T, area = 0.5, LOWER = -10, UPPER = 10, SIZE = 1000){
# Create data
x <- seq(LOWER, UPPER, length.out = SIZE)
y <- p(x)
area.vec <- c()
area.vec[1] <- 0
for(i in 2:length(x)){
x.vec <- x[1:i]
y.vec <- y[1:i]
area.vec[i] = integrate(p, lower = x[1], upper = x[i])$value
}
# Quantile
quantile = x[which.min(abs(area.vec - area))]
# Plot if requested
if(plot == TRUE){
# PDF
par(mfrow = c(1, 2))
plot(x, y, type = "l", main = "PDF", col = "indianred", lwd = 2)
grid()
# CDF
plot(x, area.vec, type = "l", main = "CDF", col = "slateblue",
xlab = "X", ylab = "CDF", lwd = 2)
# Quantile
mtext(text = paste("Quantile at ", area, "=",
round(quantile, 3)), side = 3)
grid()
par(mfrow = c(1, 1))
}
}
# Sample data
# PDF Function - Gaussian distribution
p <- function(x, SD = 1, MU = 0){
y <- (1/(SD * sqrt(2*pi)) * exp(-0.5 * ((x - MU)/SD) ^ 2))
return(y)
}
# Call to function
CDF(p, area = 0.5, LOWER = -5, UPPER = 5)