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R - Normal Distribution

In a random collection of data from independent sources, it is generally observed that the distribution of data is normal. Which means, on plotting a graph with the value of the variable in the horizontal axis and the count of the values in the vertical axis we get a bell shape curve. The center of the curve represents the mean of the data set. In the graph, fifty percent of values lie to the left of the mean and the other fifty percent lie to the right of the graph. This is referred as normal distribution in statistics.
R has four in built functions to generate normal distribution. They are described below.
dnorm(x, mean, sd)
pnorm(x, mean, sd)
qnorm(p, mean, sd)
rnorm(n, mean, sd)
Following is the description of the parameters used in above functions −
  • x is a vector of numbers.
  • p is a vector of probabilities.
  • n is number of observations(sample size).
  • mean is the mean value of the sample data. It's default value is zero.
  • sd is the standard deviation. It's default value is 1.

dnorm()

This function gives height of the probability distribution at each point for a given mean and standard deviation.
# Create a sequence of numbers between -10 and 10 incrementing by 0.1.
x <- seq(-10, 10, by = .1)

# Choose the mean as 2.5 and standard deviation as 0.5.
y <- dnorm(x, mean = 2.5, sd = 0.5)

# Give the chart file a name.
png(file = "dnorm.png")

plot(x,y)

# Save the file.
dev.off()
When we execute the above code, it produces the following result −

pnorm()

This function gives the probability of a normally distributed random number to be less that the value of a given number. It is also called "Cumulative Distribution Function".
# Create a sequence of numbers between -10 and 10 incrementing by 0.2.
x <- seq(-10,10,by = .2)
 
# Choose the mean as 2.5 and standard deviation as 2. 
y <- pnorm(x, mean = 2.5, sd = 2)

# Give the chart file a name.
png(file = "pnorm.png")

# Plot the graph.
plot(x,y)

# Save the file.
dev.off()
When we execute the above code, it produces the following result −

qnorm()

This function takes the probability value and gives a number whose cumulative value matches the probability value.
# Create a sequence of probability values incrementing by 0.02.
x <- seq(0, 1, by = 0.02)

# Choose the mean as 2 and standard deviation as 3.
y <- qnorm(x, mean = 2, sd = 1)

# Give the chart file a name.
png(file = "qnorm.png")

# Plot the graph.
plot(x,y)

# Save the file.
dev.off()
When we execute the above code, it produces the following result −

rnorm()

This function is used to generate random numbers whose distribution is normal. It takes the sample size as input and generates that many random numbers. We draw a histogram to show the distribution of the generated numbers.
# Create a sample of 50 numbers which are normally distributed.
y <- rnorm(50)

# Give the chart file a name.
png(file = "rnorm.png")

# Plot the histogram for this sample.
hist(y, main = "Normal DIstribution")

# Save the file.
dev.off()
When we execute the above code, it produces the following result −



Table of contents: 
1. R - Overview
2. R - Environment Setup
3. R - Basic Syntax
4. R - Data Types
5. R - Variables
6. R - Operators
7. R - Decision Making
8. R - Loops
9. R - Functions
10. R - Strings
11. R - Vectors
12. R - Matrices
13. R - Arrays
14. R - Factors
15. R - Data Frames
16. R - Packages
17. R - Data Reshaping
18. R - CSV Files
19. R - Excel Files
20. R - Binary Files
21. R - XML Files
22. R - JSON Files
23. R - Web Data
24. R - Database
25. R - Pie Charts
26. R - Bar Charts
27. R - Boxplots
28. R - Histograms
29. R - Line Graphs
30. R - Scatterplots
31. R - Mean, Median and Mode
32. R - Linear Regression
33. R - Multiple Regression
34. R - Logistic Regression
35. R - Normal Distribution
36. R - Binomial Distribution
37. R - Poisson Regression
38. R - Analysis of Covariance
39. R - Time Series Analysis
40. R - Nonlinear Least Square
41. R - Decision Tree
42. R - Random Forest
43. R - Survival Analysis
44. R - Chi Square Tests

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