An **Empirical Cumulative Distribution Function plot** is a statistical plot widely used to perform the comparison between multiple data sets having the same characteristics. This plot is also called the **Empirical CDF** or** ECDF** plot. MATLAB allows us to create this plot using the **cdfplot() **function.

This article is going to explore:

**What is an Empirical CDF Plot?**

**Why do we Need an Empirical CDF Plot?**

**How to Create an Empirical CDF Plot in MATLAB?**

**Example 1: How to Create an Empirical CDF Plot in MATLAB?****Example 2: How to Create an Empirical Cumulative Distribution Function Plot With an Object Handle in MATLAB?****Example 3: How to Compare Empirical CDF to Theoretical CDF Using cdfplot() Function in MATLAB?**

**What is an Empirical CDF Plot?**

An** Empirical CDF plot** is a data visualization that displays our sample data set points from lowest to highest against their percentile values. This plot needs continuous variables and calculates percentiles and other distribution properties.

**Why do we Need an Empirical CDF Plot?**

An **Empirical CDF plot** has many uses but some of its main uses are listed below.

This plot is used:

- to measure the same characteristics of multiple data sets.
- for identifying the point where most values occur.
- to find percentiles and properties of a data set.
- to identify how your data follows a best-fitted distribution.
- for assessing your data range.

**How to Create an Empirical CDF Plot in MATLAB?**

An** Empirical CDF plot** can be easily and efficiently created in MATLAB using the built-in **cdfplot() **function. This function accepts sample data in the form of a row or column vector as a mandatory parameter and creates an **Empirical CDF plot** against that data set.

**Syntax**

The **cdfplot() **function can be implemented in the following ways.

h = cdfplot(x)

Here,

The function **cdfplot(x) **is responsible for creating the **Empirical CDF plots** for the given sample data **x**. Keep in mind that **x** must be a row or column vector.

The function **h=cdfplot(x)** is responsible for creating a handle h of the **Empirical CDF plot line object**. The **handle h** can be used for querying or modifying the properties of the object after creating it.

**Example 1: How to Create an Empirical CDF Plot in MATLAB?**

This MATLAB code creates a column vector x of length 10 containing randomly distributed integers lying between 1 and 10. After that, it uses the **cdfplot()** function to create an **Empirical CDF plot** that can be seen from the given output.

cdfplot(x);

**Example 2: How to Create an Empirical Cumulative Distribution Function Plot With an Object Handle in MATLAB?**

This is another version of Example 1 in which we use the same input sample data **x **to create an **Empirical CDF plot** along its **object handle h** using **h=cdfplot(x)**. After that, we use the handle** h** to change the line style from** solid to “–” **using the** dot (.)** notation. The obtained output can be observed from the given screenshot.

h = cdfplot(x);

h.LineStyle="--"

**Example 3: How to Compare Empirical CDF to Theoretical CDF Using cdfplot() Function in MATLAB?**

In this MATLAB code, we implement the **cdfplot()** function **to perform a comparison of **the **theoretical CDF **with the **Empirical CDF**. To perform this comparison, we initialize a row vector **y** containing** 100 normally distributed random numbers** and create an **Empirical CDF plot.**

After that, we initialize another data set **x** having the** same length** as** y **containing numbers lying between **min(y)** and** max(y)**. Then we compute the** theoretical cdf x1** for the data set** x** and plot it against the values of data set **x** using the** plot() function**. We use **hold on** and** hold off **commands to create both plots on the **same figure** to observe the similarity between **Empirical CDF and theoretical CDF**.

**Conclusion**

An **Empirical CDF plot** is a statistical technique widely used to compare multiple datasets having the same characteristics. We can create this plot in MATLAB using the built-in **cdfplot()** function accepting an observed sample data set in the form of a row or column vector. This tutorial explained what is an **Empirical CDF plot** and how to create it in MATLAB using the **cdfplot() **function.