rnorm()
rnorm() is a popular function in R that generates random numbers using normal distribution. Normal distribution, also called Gaussian distribution, represents a bell-shaped curve with the maximum values clustered around the mean value.
The Probability Density function of a normal distribution is given by:
f(x| μ, σ2 ) = 1/√2πσ2 e-(x-μ)2 / 2σ2
where,
- x is a random variable
- μ is the mean value
- σ2 is the standard deviation
rnorm() function takes three parameters. The standard parameter for this function is given by:
R
rnorm(n, mean = 0, sd = 1) |
where,
- n= number of random numbers to be generated
- mean: The mean of the normal distribution. Default is 0.
- sd: The standard deviation of the normal distribution. Default is 1.
The mean parameter decides the center of the distribution while the sd parameter defines the spread of the distribution. We can understand this with the help of a random example and also plot it to understand how this distribution works.
R
# Generate 100 random numbers from a normal distribution with mean 0 and sd 1random_numbers <- rnorm(100, mean = 0, sd = 1)# Plot a histogram of the random numbershist(random_numbers, freq = FALSE, col = "skyblue", main = "Histogram of Random Numbers from Normal Distribution", xlab = "Random Numbers", ylab = "Density")# Add a density curve to the histogramlines(density(random_numbers), col = "red", lwd = 2) |
Output:
Difference Between rnorm() and runif() in R
The above curve is bell-shaped since it is a normal distribution.
Analysis of Height in Adults using rnorm()
Suppose we want to analyze the height of the individuals in a particular country and we need to generate a dataset that closely resembles the actual height of the people in that country. For this purpose, we can use the rnorm() function to analyze the height, average height, standard deviation of height, and the category where most of the heights will fall.
R
# Define parameters based on real-world data or estimatesmean_height <- 170 # Mean height in centimeterssd_height <- 10 # Standard deviation of heights# Generate a dataset of 1000 random heightsheight_data <- rnorm(1000, mean = mean_height, sd = sd_height)# Analyze the generated datamean_height_generated <- mean(height_data)median_height_generated <- median(height_data)#to view the first 6 rows of the datasethead(height_data) |
Output:
[1] 166.6658 171.7388 156.5240 170.6069 170.0746 175.0088
Visualize the distribution of heights
R
# Visualize the distribution of heightshist(height_data, breaks = 20, col = "skyblue", main = "Distribution of Heights", xlab = "Height (cm)", ylab = "Frequency")# Add mean and median lines to the histogramabline(v = mean_height_generated, col = "red", lwd = 2, lty = 2)abline(v = median_height_generated, col = "blue", lwd = 2, lty = 2)# Add legendlegend("topright", legend = c("Mean", "Median"), col = c("red", "blue"), lty = 2, lwd = 2) |
Output:
Difference Between rnorm() and runif() in R
This dataset closely resembles real-world observations and allows us to perform various statistical analyses and visualizations, providing insights into the distribution of heights and the characteristics of the population.
The Difference Between rnorm() and runif() in R
While conducting statistical analysis we generate random numbers for reproducibility and experiments. R Programming Language provides two functions runif() and rnorm() to generate random functions. In this article, we will understand the difference between these two functions and how we can use them with the help of examples.