Introduction
R provides functions for working with probability distributions. These are essential for statistical modeling.
Common Distributions
# Normal distribution
dnorm(x, mean = 0, sd = 1) # Density
pnorm(q, mean = 0, sd = 1) # CDF
qnorm(p, mean = 0, sd = 1) # Quantile
rnorm(n, mean = 0, sd = 1) # Random sample
# Binomial
dbinom(x, size, prob) # Density
pbinom(q, size, prob) # CDF
qbinom(p, size, prob) # Quantile
rbinom(n, size, prob) # Random sample
# Poisson
dpois(x, lambda) # Density
ppois(q, lambda) # CDF
qpois(p, lambda) # Quantile
rpois(n, lambda) # Random sample
# Exponential
dexp(x, rate = 1) # Density
pexp(q, rate = 1) # CDF
qexp(p, rate = 1) # Quantile
rexp(n, rate = 1) # Random sample
Distribution Plots
# Normal distribution plot
x <- seq(-3, 3, length = 100)
y <- dnorm(x)
plot(x, y, type = "l")
# Histogram with distribution
hist(rnorm(1000), probability = TRUE)
curve(dnorm(x), add = TRUE)
Summary
R provides functions for many distributions. Use d/p/q/r functions for density, CDF, quantile, and random generation.