The triangular distribution is a continuous distribution defined on the range with probability density function
(1)
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(2)
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where is the mode.
The symmetric triangular distribution on is implemented in the Wolfram Language as TriangularDistribution[a, b], and the triangular distribution on with mode as TriangularDistribution[a, b, c].
The mean is
(3)
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the raw moments are
(4)
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(5)
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and the central moments are
(6)
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(7)
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(8)
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It has skewness and kurtosis excess given by
(9)
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(10)
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