Probability Distributions

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.