## Industrial and Management Systems Engineering

#### Title

Impact of Sample Size on Approximating the Triangular Distribution

#### Date of this Version

2-2010

#### Abstract

The triangular distribution is used in discrete-event and Monte Carlo simulation as a key probability distribution for modeling randomness. This demonstration, written in Mathematica, compares the sample triangular probability distribution with the theoretical distribution. Probability and statistical theory shows us that as the number of samples increases for the given parameter values, the more closely the sample probability distribution will resemble the theoretical distribution. You can verify this by specifying the minimum, mode, and maximum parameter values that describe a sample triangular probability distribution. The specified number of samples is randomly generated and compared to the theoretical distribution.

In the demonstration, a user can select the minimum, mode, and maximum parameter values for the triangular distribution. By definition, the minimum < mode < maximum. The sample probability distribution is compared to the theoretical distribution as a user increases the sample size. In general, as the sample size increases, the more closely the sample distribution matches the theoretical distribution. The red dot shows the mean value for the theoretical distribution.

## Comments

P. Savory (2010), “Impact of Sample Size on Approximating the Triangular Distribution”, Mathematica Software Demonstration, The Wolfram Demonstations Project. Available at: http://demonstrations.wolfram.com/ImpactOfSampleSizeOnApproximatingTheTriangularDistribution/