The dnorm() function in R is a function in the norm family function (`dnorm()`

, `pnorm()`

, `qnorm()`

, `rnorm()`

). The function() calculates the normal distribution’s probability density function (PDF). Keep reading the article, and we will show you how to use the function.

## Normal distribution and probability density function (PDF)

Before learning about the dnorm() function, we will remind you of the normal distribution and its probability density function (PDF).

A continuous random variable x is said to have the normal distribution with the mean \mu and the standard deviation \sigma > 0 , if the probability density function (PDF) is:

` \frac { 1 } { \sqrt { 2 \pi } \sigma } e^{ -(x - \mu)^2/2 \sigma^2} `

**The dnorm() function **

Make sure that you remember the normal distribution and the probability density function. Next, we will discover the `dnorm()`

function.

**Syntax:**

`dnorm(x, mean, sd)`

**Parameters:**

**x**: A random variable vector**mean**: The mean of the vector’s elements**sd**: The standard deviation of the vector’s elements

**Some examples of the dnorm() function**

Below are a few examples of using the `dnorm()`

function to calculate and represent the normal distribution and its probability density values.

**Calculate the probability density function of the normal distribution**

Because the normal distribution distributes balance around zero, we will create a vector having elements from -5 to 5. Then, use the dnorm() function to calculate the probability density values of the vector with a mean equal to 0 and a standard deviation equal to 1. Finally, we get the results symmetrical by the middle value.

**Code:**

# Create a vector x having balance values around 0 x <- seq(-5, 5, by = 1) # Calculate the probability density of the vector x y <- dnorm(x, mean = 0, sd = 1) cat("The probability density values of x are:\n") cat(y)

**Result:**

```
The probability density values of x are:
1.48672e-06 0.0001338302 0.004431848 0.05399097 0.2419707 0.3989423 0.2419707 0.05399097 0.004431848 0.0001338302 1.48672e-06
```

**Visualize the probability density function of the normal distribution**

To be more intuitive, we will visualize the results by using the `plot()`

function.

**Code:**

# Create a vector x having balance values around 0 x <- seq(-5, 5, by = 0.0001) # Calculate the probability density of the vector x y <- dnorm(x) plot(y, col = "red", main = "The probability density values of the vector x", col.main = "blue")

**Result:**

## Summary

In summary, the dnorm() function calculates the value of the probability density function of the normal distribution. Although the function is simple, it has many applications in practice. We hope you understand both knowledge in math and programming.

**Maybe you are interested**:

- The complete.cases() function in R
- ncol in R: Count the number of the columns in the R object
- nrow in R: The number of rows in the R object

My name is Robert Collier. I graduated in IT at HUST university. My interest is learning programming languages; my strengths are Python, C, C++, and Machine Learning/Deep Learning/NLP. I will share all the knowledge I have through my articles. Hope you like them.

**Name of the university: **HUST

**Major**: IT

**Programming Languages**: Python, C, C++, Machine Learning/Deep Learning/NLP