How to Use the Triangular Distribution in R (With Examples)


The triangular distribution is a continuous probability distribution with a probability density function shaped like a triangle.

It is defined by three values:

  • The minimum value a
  • The maximum value b
  • The peak value c

Triangular distribution

To calculate probabilities for the triangular distribution in R we can use the ptri() function from the EnvStats package, which uses the following syntax:

ptri(q, min = 0, max = 1, mode = 1/2)

where:

  • q: Quantile of interest
  • min: The minimum value of the distribution
  • max: The maximum value of the distribution
  • mode: The peak value of the distribution

The following examples show how to use this function in practice in R.

Example 1: Calculating Probability Less Than Some Value

Suppose a restaurant estimates that their total sales for the upcoming week will be a minimum of $10,000, a maximum of $30,000, and most likely $25,000.

What is the probability that the restaurant makes less than $20,000 total sales?

We can use the following code to calculate this probability:

library(EnvStats)

#calculate probability
ptri(q = 20000, min = 10000, max = 30000, mode = 25000)

[1] 0.3333333

The probability that the restaurant makes less than $20,000 total sales is .333.

Example 2: Calculating Probability Greater Than Some Value

Suppose a shop estimates that the number of customers that will enter in a given week will be a minimum of 500, a maximum of 2,000, and most likely 1,200.

What is the probability that more than 1,500 customers enter the shop in a given week?

We can use the following code to calculate this probability:

library(EnvStats)

#calculate probability
1 - ptri(q = 1500, min = 500, max = 2000, mode = 1200)

[1] 0.2083333

The probability that more than 1,500 customers enter the shop is about .208.

Note: You can find the complete documentation for the ptri() function here.

Additional Resources

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

How to Use the Normal Distribution in R
How to Use the Binomial Distribution in R
How to Use the Poisson Distribution in R
How to Use the Multinomial Distribution in R

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