TriangularDistribution

Generate a set of random numbers that are triangularly distributed:

Compare its histogram to the PDF:

Distribution parameters estimation:

Estimate the distribution parameters from sample data:

Compare the density histogram of the sample with the PDF of the estimated distribution:

Skewness varies with the shape parameter c:

Skewness is 0 in the symmetric case:

Kurtosis is constant:

Different moments with closed forms as functions of parameters:

Moment:

Moment has closed form:

CentralMoment:

Closed form for symbolic order:

FactorialMoment:

Cumulant:

Hazard function:

Quantile function:

An executive is given an account of historical seasonal demands for a product in million units. The minimum, maximum, and most likely demands are 1, 1.4, and 1.25, respectively. Find the expected demand and its standard deviation using TriangularDistribution:

The momentum of a secondary particle from a synchrotron beam is modeled by TriangularDistribution:

The distribution is symmetric and attains maximum at :

Find momenta where distribution density is at half-height:

Find the full width at half-height:

Parameter influence on the CDF for each :

Triangular distribution is closed under translation and scaling by a positive factor:

Relationships to other distributions:

The mean of two uniform variables follows TriangularDistribution:

Triangular distribution is a special case of BatesDistribution:

The default position for c is in the middle of the support interval:

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: