Triangledf

Purpose

Triangle distribution.

Synopsis

prob = triangledf(function,x,a,b,c)

Description

Estimates cumulative distribution function (cumulative, cdf), probability density function (density, pdf), quantile (inverse of cdf), or random numbers for a Triangle distribution.

This distribution is usually used for rough models of data and is triangular in shape (hence the name).

$f(x)={\frac {2\left(x-a\right)}{\left(b-a\right)\left(c-a\right)}}\mathrm {I} \left(a\leq x\leq c\right)+{\frac {2\left(b-x\right)}{\left(b-a\right)\left(b-c\right)}}\mathrm {I} \left(c\leq x\leq b\right)$

$F(x)={\frac {\left(x-a\right)^{2}}{\left(b-a\right)\left(c-a\right)}}\mathrm {I} \left(a\leq x\leq c\right)+1-{\frac {\left(b-x\right)^{2}}{\left(b-c\right)\left(c-a\right)}}\mathrm {I} \left(c\leq x\leq b\right)$

Inputs

• function = [ {'cumulative'} | 'density' | 'quantile' | 'random' ], defines the functionality to be used. Note that the function recognizes the first letter of each string so that the string could be: [ 'c' | 'd' | 'q' | 'r' ].

• x = matrix in which the sample data is stored (-inf,inf).

for function = 'quantile' - interval (0,1).

for function = 'random' - vector indicating the size of the random matrix to create.

• a = "min" parameter (real, <= mode).
• b = "max" parameter (real, >= mode).
• c = "mode" parameter (real, >= min and <=max).

Note: If inputs (x, a, b, and c) are not equal in size, the function will attempt to resize all inputs to the largest input using the RESIZE function.

Note: Functions will typically allow input values outside of the acceptable range to be passed but will convert them to NaN.

Examples

Cumulative

>> prob = triangledf('c',2,1,3,2)
prob =
    0.5000
>> x    = [0:0.1:10];
>> plot(x,triangledf('c',x,1,3,2),'b-',x,triangledf('c',x,1,5,3),'r-')

Density

>> prob = triangledf('d',2,1,3,2)
prob =
    1.0000
>> x    = [0:0.1:10];
>> plot(x,triangledf('d',x,0,3,0),'b-',x,triangledf('d',x,1,3,2),'r-')

Quantile

>> prob = triangledf('q',0.5,1,3,2)
prob =
    2.0000

Random

>> prob = triangledf('r',[4 1],1,3,2)
ans =
    2.2817
    1.9431
    2.1094
    2.2585

See Also

betadf, cauchydf, chidf, expdf, gammadf, gumbeldf, laplacedf, logisdf, lognormdf, normdf, paretodf, raydf, unifdf, weibulldf