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# TriangularDistribution

 TriangularDistribution represents a symmetric triangular statistical distribution giving values between min and max. TriangularDistributionrepresents a triangular distribution with a maximum at c.
• The mean of a pair of uniformly distributed random variables follows a symmetric triangular distribution. »
Probability density function:
Cumulative distribution function:
Mean and variance:
Median:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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Median:
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 Scope   (7)
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 has closed form:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (2)
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:
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