Contents

prob.TriangularDistribution class

Package: prob
Superclasses: prob.ParametricTruncatableDistribution

Triangular probability distribution object

Description

prob.TriangularDistribution is an object consisting of parameters and a model description for a triangular probability distribution. Create a probability distribution object with specified parameters using makedist.

Construction

pd = makedist('Triangular') creates a triangular probability distribution object using the default parameter values.

pd = makedist('Triangular','a',a,'b',b,'c',c) creates a triangular distribution object using the specified parameter values.

Input Arguments

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a — Lower limit0 (default) | scalar value

Lower limit for the triangular distribution, specified as a scalar value.

Data Types: single | double

b — Peak location0.5 (default) | scalar value

Peak location for the triangular distribution, specified as a scalar value greater than or equal to a.

Data Types: single | double

c — Upper limit1 (default) | scalar value

Upper limit for the triangular distribution, specified as a scalar value greater than or equal to b.

Data Types: single | double

Properties

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aLower limitscalar value

Lower limit for the triangular distribution, stored as a scalar value.

Data Types: single | double

bPeak locationscalar value

Location of the peak for the triangular distribution, stored as a scalar value greater than or equal to a.

Data Types: single | double

cUpper limitscalar value

Upper limit for the triangular distribution, stored as a scalar value greater than or equal to b.

Data Types: single | double

DistributionNameProbability distribution nameprobability distribution name string

Probability distribution name, stored as a valid probability distribution name string. This property is read-only.

Data Types: char

IsTruncatedLogical flag for truncated distribution0 | 1

Logical flag for truncated distribution, stored as a logical value. If IsTruncated equals 0, the distribution is not truncated. If IsTruncated equals 1, the distribution is truncated. This property is read-only.

Data Types: logical

NumParametersNumber of parameterspositive integer value

Number of parameters for the probability distribution, stored as a positive integer value. This property is read-only.

Data Types: single | double

ParameterDescriptionDistribution parameter descriptionscell array of strings

Distribution parameter descriptions, stored as a cell array of strings. Each cell contains a short description of one distribution parameter. This property is read-only.

Data Types: char

ParameterNamesDistribution parameter namescell array of strings

Distribution parameter names, stored as a cell array of strings. This property is read-only.

Data Types: char

ParameterValuesDistribution parameter valuesvector of scalar values

Distribution parameter values, stored as a vector. This property is read-only.

Data Types: single | double

TruncationTruncation intervalvector of scalar values

Truncation interval for the probability distribution, stored as a vector containing the lower and upper truncation boundaries. This property is read-only.

Data Types: single | double

Methods

Inherited Methods

cdf Cumulative distribution function of probability distribution object
icdfInverse cumulative distribution function of probability distribution object
iqrInterquartile range of probability distribution object
median Median of probability distribution object
pdfProbability density function of probability distribution object
randomGenerate random numbers from probability distribution object
truncateTruncate probability distribution object
meanMean of probability distribution object
std Standard deviation of probability distribution object
varVariance of probability distribution object

Definitions

Triangular Distribution

The triangular distribution is frequently used in simulations when limited sample data is available. The lower and upper limits represent the smallest and largest values, and the location of the peak represents an estimate of the mode.

The triangular distribution uses the following parameters.

ParameterDescriptionSupport
aLower limitab
bPeak locationabc
cUpper limitcb

The probability density function (pdf) is

f(x|a,b,c)={2(xa)(ca)(ba);axb2(cx)(ca)(cb);b<xc0;x<a,x>c.

and

f(x|a,b,c)=2(cx)(ca)(cb);b<xc.

The value of the pdf is 0 when x < a or x > c.

Examples

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Create a Triangular Distribution Object Using Default Parameters

Create a triangular distribution object using the default parameter values.

pd = makedist('Triangular')
pd = 

  TriangularDistribution

A = 0, B = 0.5, C = 1

Create a Triangular Distribution Object Using Specified Parameters

Create a triangular distribution object by specifying parameter values.

pd = makedist('Triangular', 'a',-2,'b',1,'c',5)
pd = 

  TriangularDistribution

A = -2, B = 1, C = 5

Compute the mean of the distribution.

m = mean(pd)
m =

    1.3333
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