# Plot Cumulative Distribution Function in R

In this article, we will discuss how to plot a cumulative distribution function (CDF) in the R programming Language.

The cumulative distribution function (CDF) of a random variable evaluated at x, is the probability that x will take a value less than or equal to x. To calculate the cumulative distribution function in the R Language, we use the ecdf() function. The ecdf() function in R Language is used to compute and plot the value of the Empirical Cumulative Distribution Function of a numeric vector. The ecdf() function takes the data vector as an argument and returns the CDF data.

Syntax:ecdf( data_vector )

Parameter:

data_vector:determines the vector that contains data for CDF calculation.

## Plot cumulative distribution function in base R

To plot a CDF function in base R, we first calculate the CDF by using the ecdf() function. Then we use the plot() function to plot the CDF plot in the R Language. The plot function takes the result of the ecdf() function as an argument to plot the CDF plot.

Syntax:plot( CDF )

Parameter:

CDF:determines the cumulative distribution function calculated using the ecdf() function.

**Example 1: C**umulative distribution function in base R

Here, is an example of a basic Cumulative Distribution Function Plot in the R Language.

## R

`# create sample data` `sample_Data = ` `rnorm` `(500)` ` ` `# calculate CDF ` `CDF <- ` `ecdf` `(sample_Data )` ` ` `# draw the cdf plot` `plot` `( CDF )` |

**Output:**

### Example 2: **C**umulative distribution function in base R using iris dataset

## R

`head` `(iris)` `plot` `(` `ecdf` `(iris$Petal.Length))` |

**Output:**

## Plot CDF of Known Distribution

To plot the cumulative distribution function of a standard distribution in a specific known range, we use the curve() function in the R Language. The curve() function draws a curve corresponding to a function over the interval. It takes an expression as an argument that in this case will be pnorm along with the limits from and to and returns a Normal CDF Plot.

Syntax:curve( expression, from, to )

Parameters:

expression:determines the expression function for CDF calculation.from:determines the lower limit of data.to:determines the upper limit of data.

**Example:**

Here, is an example of a normal CDF plot.

## R

`# plot normal CDF plot` `curve` `(pnorm, from = -10, to = 10)` |

**Output:**

## Plot CDF of Known Distribution using ggplot2 Package

To draw the same plot in the ggplot2 package library, we use the stat_function() function. The stat_function takes the expression function as a fun argument and converts the curve according to that expression in a basic ggplot2 plot.

Syntax:plot + stat_function( fun )

Parameters:

fun:determines the function for the shape of the plot.

**Example:**

Here, is an example of a normal CDF plot using ggplot2.

## R

`# load library ggplot2` `library` `(ggplot2)` ` ` `# create sample dataframe for upper and lower limit` `sample_limit<- ` `data.frame` `(x = ` `c` `(-10, 10))` ` ` `# draw CDF Plot` `ggplot` `(sample_limit, ` `aes` `(x = x)) +` ` ` `stat_function` `(fun = pnorm)` |

**Output:**