The exponential distribution is a probability distribution that is used to model the time we must wait until a certain event occurs.

If a random variable *X* follows an exponential distribution, then the **probability density function** of *X* can be written as:

*f*(x; λ) = λe^{-λx}

where:

**λ:**the rate parameter**e:**A constant roughly equal to 2.718

The **cumulative distribution function** of *X* can be written as:

*F*(x; λ) = 1 – e^{-λx}

This tutorial explains how to plot a PDF and CDF for the exponential distribution in R.

**Plotting a Probability Density Function**

The following code shows how to plot a PDF of an exponential distribution with rate parameter λ = 0.5:

curve(dexp(x, rate = .5), from=0, to=10, col='blue')

The following code shows how to plot multiple PDF’s of an exponential distribution with various rate parameters:

#plot PDF curves curve(dexp(x, rate = .5), from=0, to=10, col='blue') curve(dexp(x, rate = 1), from=0, to=10, col='red', add=TRUE) curve(dexp(x, rate = 1.5), from=0, to=10, col='purple', add=TRUE) #add legend legend(7, .5, legend=c("rate=.5", "rate=1", "rate=1.5"), col=c("blue", "red", "purple"), lty=1, cex=1.2)

**Plotting a Cumulative Distribution Function**

The following code shows how to plot a CDF of an exponential distribution with rate parameter λ = 0.5:

curve(pexp(x, rate = .5), from=0, to=10, col='blue')

The following code shows how to plot multiple CDF’s of an exponential distribution with various rate parameters:

#plot CDF curves curve(pexp(x, rate = .5), from=0, to=10, col='blue') curve(pexp(x, rate = 1), from=0, to=10, col='red', add=TRUE) curve(pexp(x, rate = 1.5), from=0, to=10, col='purple', add=TRUE) #add legend legend(7, .9, legend=c("rate=.5", "rate=1", "rate=1.5"), col=c("blue", "red", "purple"), lty=1, cex=1.2)

**Additional Resources**

The following tutorials explain how to plot other probability distributions in R:

How to Plot a Poisson Distribution in R

How to Plot a Binomial Distribution in R

How to Plot a t Distribution in R

How to Plot a Normal Distribution in R

How to Plot a Chi-Square Distribution in R