Statistics[Distributions]
Triangular
triangular distribution
Calling Sequence
Parameters
Description
Examples
References
Triangular(a, b, c)
TriangularDistribution(a, b, c)
a
-
lower bound
b
upper bound
c
distribution mode
The triangular distribution is a continuous probability distribution with probability density function given by:
ft=0t<a2t−ab−ac−at≤c2b−tb−a−c+bt≤b0otherwise
subject to the following conditions:
a≤c,c≤b,a<b
Note that the Triangular command is inert and should be used in combination with the RandomVariable command.
withStatistics:
X≔RandomVariableTriangulara,b,c:
PDFX,u
0u<a2u−ab−ac−au≤c2b−ub−a−c+bu≤b0otherwise
PDFX,0.5
0.0.5<a2.0.5−1.ab−1.ac−1.a0.5≤c2.b−0.5b−1.ab−1.c0.5≤b0.otherwise
MeanX
a3+b3+c3
VarianceX
118a2+118b2+118c2−118ab−118ac−118bc
Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.
Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.
Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
See Also
Statistics
Statistics[RandomVariable]
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