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# 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.

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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

 a Lower limit for the triangular distribution, stored as a scalar value. b Location of the peak for the triangular distribution, stored as a scalar value greater than or equal to a. c Upper limit for the triangular distribution, stored as a scalar value greater than or equal to b. DistributionName Name of the probability distribution, stored as a valid probability distribution name string. This property is read-only. IsTruncated 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. NumParameters Number of parameters for the probability distribution, stored as a positive integer value. This property is read-only. ParameterDescription Descriptions of distribution parameters, stored as a cell array of strings. Each cell contains a short description of one distribution parameter. This property is read-only. ParameterNames Names of distribution parameters, stored as a cell array of strings. This property is read-only. ParameterValues Values of distribution parameters, stored as a vector. This property is read-only. Truncation Truncation interval for the probability distribution, stored as a vector containing the lower and upper truncation boundaries. This property is read-only.

## Methods

### Inherited Methods

 cdf Cumulative distribution function of probability distribution object icdf Inverse cumulative distribution function of probability distribution object iqr Interquartile range of probability distribution object median Median of probability distribution object pdf Probability density function of probability distribution object random Generate random numbers from probability distribution object truncate Truncate probability distribution object
 mean Mean of probability distribution object std Standard deviation of probability distribution object var Variance 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 limit
bPeak location
cUpper limit

The probability density function (pdf) is

and

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```