# R - Normal Distribution

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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