Built-in Mathematica Symbol

TriangularDistribution

TriangularDistribution[{min, max}]
represents a symmetric triangular statistical distribution giving values between min and max.

TriangularDistribution[{min, max}, c]
represents a triangular distribution with a maximum at c.

The mean of a pair of uniformly distributed random variables follows a symmetric triangular distribution. »

TriangularDistribution allows min, max and c to be any real numbers such that min<c<max.

TriangularDistribution can be used with such functions as Mean, CDF and RandomReal. »

The mean and variance of a symmetric triangular distribution:

Probability density function:

The mean and variance of a symmetric triangular distribution:

Probability density function:

Generate a set of random numbers that are triangularly distributed:

Properties based on higher-order moments:

The q

quantile of a triangular distribution:

Plot the cumulative distribution function of the random variable:

A contour plot as both x and max are varied:

The probability density function integrates to unity:

Moments can be obtained from the characteristic function:

The Mean of 2 random variables from UniformDistribution follows a triangular distribution:

TriangularDistribution is not defined when min or max is not real:

TriangularDistribution is not defined when c is not between min and max:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful: