Triangular Distribution
X ~ Triangular(a, c, b)
Bounded / Risk-Modeling Family • Published July 22, 2026
The three-number distribution behind PERT project scheduling and Monte Carlo risk analysis: a piecewise-linear density set directly by a minimum, mode, and maximum with no shape-fitting required, an exact sum-of-two-Uniforms construction that previews the Central Limit Theorem, and a mode with no closed-form maximum-likelihood estimator (verified via grid search) that nonetheless beats the closed-form method-of-moments estimator on efficiency.
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About This Reference Sheet
The three-number distribution behind PERT project scheduling and Monte Carlo risk analysis: a piecewise-linear density set directly by a minimum, mode, and maximum with no shape-fitting required, an exact sum-of-two-Uniforms construction that previews the Central Limit Theorem, and a mode with no closed-form maximum-likelihood estimator (verified via grid search) that nonetheless beats the closed-form method-of-moments estimator on efficiency.
Support
x ∈ [a, b]
Parameters
a < b (min, max), c ∈ [a,b] (mode)