Introduction to Normal Distribution Functions

• dnorm(): Density function
• pnorm(): Cumulative distribution function
• qnorm(): Quantile function
• rnorm(): Random number generation

These functions are essential for working with the normal distribution in R.

dnorm(): Density Function

• Purpose: Computes the probability density function (PDF) of the normal distribution.
• Syntax: dnorm(x, mean = 0, sd = 1)

x <- seq(-4, 4, length.out = 100)
density <- dnorm(x, mean = 0, sd = 1)
plot(x, density, type = "l", main = "dnorm(): Normal Density Function", xlab = "x", ylab = "Density")

pnorm(): Cumulative Distribution Function

• Purpose: Computes the cumulative probability up to a given value.
• Syntax: pnorm(q, mean = 0, sd = 1)

x <- seq(-4, 4, length.out = 100)
cdf <- pnorm(x, mean = 0, sd = 1)
plot(x, cdf, type = "l", main = "pnorm(): Cumulative Distribution Function", xlab = "x", ylab = "Cumulative Probability")

qnorm(): Quantile Function

• Purpose: Computes the quantile (inverse of pnorm()).
• Syntax: qnorm(p, mean = 0, sd = 1)

p <- seq(0, 1, length.out = 100)
quantiles <- qnorm(p, mean = 0, sd = 1)
plot(p, quantiles, type = "l", main = "qnorm(): Quantile Function", xlab = "Probability", ylab = "Quantile")

rnorm(): Random Number Generation

• Purpose: Generates random numbers from a normal distribution.
• Syntax: rnorm(n, mean = 0, sd = 1)

set.seed(123)
random_numbers <- rnorm(1000, mean = 0, sd = 1)
hist(random_numbers, breaks = 30, main = "rnorm(): Random Numbers from Normal Distribution", xlab = "Value", col = "lightblue")

Summary

• dnorm(): Gives the height of the PDF at a specific point.
• pnorm(): Gives the cumulative probability up to a point.
• qnorm(): Finds the value corresponding to a given cumulative probability.
• rnorm(): Generates random numbers from a normal distribution.

These functions are fundamental for statistical analysis and simulations in R.

Questions?