# Create a sequence of values between -10 and 10 with a difference of 0.1 x <- seq(-10, 10, by=0.1) y <- dnorm(x, mean(x), sd(x)) plot(x, y, type="l") abline(v=mean(x), col="red")
dnorm() calculates the density function of a normal distribution.
# Create a sequence of values between -10 and 10 with a difference of 0.1 x <- seq(-10, 10, by=0.1) y <- dnorm(x, mean(x), sd(x)) plot(x, y, type="l") abline(v=mean(x), col="red")
pnorm() calculates the cumulative distribution function.
x <- seq(-10, 10, by=0.1) y <- pnorm(x, mean(x), sd(x)) plot(x, y, type="l")
qnorm() is the inverse of pnorm(). It takes the probability value and gives output which corresponds to the probability value. It is useful in finding the percentiles of a normal distribution.
x <- seq(0, 1, by=0.02) y <- qnorm(x, mean(x), sd(x)) plot(x, y, type="l")
rnorm() is used to generate a vector of random numbers which are normally distributed.
# Create a vector of 1000 random numbers with mean=10 and sd=5 set.seed(1) x <- rnorm(1000, mean=10, sd=5) # Create a histogram with probability=TRUE in order to add a normal curve or a density line hist(x, probability=TRUE)
# X-axis grid x2 <- seq(min(x), max(x), length=50) fun <- dnorm(x2, mean(x), sd(x)) hist(x, probability=TRUE, ylim = c(0, max(fun)), main="Histogram with normal curve") lines(x2, fun, col="red", lwd=1.5)
hist(x, probability=TRUE, ylim = c(0, max(fun)), main="Histogram with density curve") lines(density(x), col="red", lwd=1.5)
The easiest way to simulate a bivariate normal distribution in R is to use the mvrnorm() function from the MASS package.
library(MASS) set.seed(1) bidata <- as.data.frame(mvrnorm(n=100, mu=c(0, 0), Sigma=matrix(c(2, -1, -1, 1), ncol=2))) head(bidata)
V1 V2 1 1.0638091 -0.2067474 2 -0.2664476 0.1340747 3 1.4461205 -0.2319283 4 -2.2470623 1.2739463 5 -0.2408411 0.6244316 6 0.5550514 -1.6270500
The easiest way to plot a bivariate normal distribution in R is to use functions from the mnormt() package. To create a contour plot, which offers a 2-D visualization of a bivariate normal distribution, we use the contour() function.
library(mnormt) set.seed(1) # Create a bivariate normal distribution x <- seq(-3, 3, 0.1) y <- seq(-3, 3, 0.1) mu <- c(0, 0) sigma <- matrix(c(2, -1, -1, 2), nrow=2) f <- function(x, y) dmnorm(cbind(x, y), mu, sigma) z <- outer(x, y, f) # Create the contour plot contour(x, y, z)
We also use the persp() function to create a surface plot, which offers a 3-D visualization of a bivariate normal distribution.
persp(x, y, z, theta=-30, phi=20, col="blue", expand=0.7, ticktype="detailed")
# theta, phi: Defines the angles of the viewing direction # expand: Controls the size of the z-axis # ticktype: Controls the appearance of the ticks on the axes