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Statistics[Distributions]

  

Triangular

  

triangular distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

Triangular(a, b, c)

TriangularDistribution(a, b, c)

Parameters

a

-

lower bound

b

-

upper bound

c

-

distribution mode

Description

• 

The triangular distribution is a continuous probability distribution with probability density function given by:

ft&equals;piecewiset<a&comma;0&comma;tc&comma;2tabaca&comma;tb&comma;2btbac&plus;b&comma;0

  

subject to the following conditions:

ac&comma;cb&comma;a<b

• 

Note that the Triangular command is inert and should be used in combination with the RandomVariable command.

Examples

withStatistics&colon;

XRandomVariableTriangulara&comma;b&comma;c&colon;

PDFX&comma;u

&lcub;0u<a2uabacauc2bubac&plus;bub0otherwise

(1)

PDFX&comma;0.5

&lcub;0.0.5<a2.0.51.ab1.ac1.a0.5c2.b0.5b1.ab1.c0.5b0.otherwise

(2)

MeanX

13a&plus;13b&plus;13c

(3)

VarianceX

118a2&plus;118b2&plus;118c2118ab118ac118bc

(4)

References

  

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[Distributions]

Statistics[RandomVariable]