The Triangular Distribution

The triangular distribution can be used to model a variable for which very little data is available. Using an estimate for the minimum and maximum value as well as the mode (most common value), a reasonable approximation can be made.

The triangular distribution has three parameters: the minimum value, the maximum value, and the mode. The traditional types of parameters (location, scale, shape) don't have an obvious meaning for the triangular distribution. The probability density function is:

The triangular distribution is implemented by the TriangularDistribution class. It has three constructors. The first constructor takes just one argument: the mode. The minimum and maximum values are set to 0 and 1, respectively. The second constructor takes two arguments and adds the maximum value. Finally, the third constructor takes three arguments: the minimum, the maximum, and the mode (most likely value).

The following constructs the same triangular distribution over the interval [0, 1] with mode 0.6:

var triangular1 = new TriangularDistribution(0.6);
var triangular2 = new TriangularDistribution(1.0, 0.6);
var triangular3 = new TriangularDistribution(0.0, 1.0, 0.6);

Dim triangular1 = New TriangularDistribution(0.6)
Dim triangular2 = New TriangularDistribution(1.0, 0.6)
Dim triangular3 = New TriangularDistribution(0.0, 1.0, 0.6)

let triangular1 = TriangularDistribution(0.6)
let triangular2 = TriangularDistribution(1.0, 0.6)
let triangular3 = TriangularDistribution(0.0, 1.0, 0.6)

The TriangularDistribution class has three specific properties, LowerBound, UpperBound, and Mode, which return the three parameters of the distribution.

TriangularDistribution has one static (Shared in Visual Basic) method, Sample, which generates a random sample using a user-supplied uniform random number generator. The second and third parameters are the location and scale parameters of the distribution.

var random = new MersenneTwister();
double sample = TriangularDistribution.Sample(random, 6.8, 1.8);

Dim random = New MersenneTwister()
Dim sample = TriangularDistribution.Sample(random, 6.8, 1.8)

let random = MersenneTwister()
let sample = TriangularDistribution.Sample(random, 6.8, 1.8)

The above example uses the MersenneTwister class to generate uniform random numbers.

For details of the properties and methods common to all continuous distribution classes, see the topic on continuous distributions..