makedist

Create probability distribution object

Syntax

pd = makedist(distname)

pd = makedist(distname,Name,Value)

list = makedist

Description

pd = makedist(distname) creates a probability distribution object for the distribution distname, using the default parameter values.

Use makedist to specify uniform, normal, multinomial, piecewise linear, or triangular distribution objects. If you have Statistics and Machine Learning Toolbox™ software, you can use makedist to create objects for other distributions, such as the Gamma or Weibull distributions. For more information, see makedist (Statistics and Machine Learning Toolbox).

To truncate the probability distribution to a specified interval, use truncate (Statistics and Machine Learning Toolbox).

pd = makedist(distname,Name,Value) creates a probability distribution object with one or more distribution parameter values specified by name-value pair arguments.

list = makedist returns a cell array list containing a list of the probability distributions that makedist can create.

Examples

Create Normal Distribution Object

Create a normal distribution object using default parameter values.

pd = makedist('Normal')

pd = 
  NormalDistribution

  Normal distribution
       mu = 0
    sigma = 1

Specify Parameters for a Normal Distribution Object

Create a normal distribution object with a mean value of mu = 75, and a standard deviation of sigma = 10.

pd = makedist('Normal','mu',75,'sigma',10);

Specify Piecewise Linear Distribution Object

Create a piecewise linear distribution object for a distribution with values from 6 to 10, where values from 6 to 8 are four times more likely than values from 8 to 10.

pd = makedist('PieceWiselinear','x',[6 8 10],'Fx',[0 0.8 1]);

You specify the cumulative distribution function Fx as [0 0.8 1] because the difference between 0.8 and 0 is four times the difference between 1 and 0.8. As a result, the generated distribution has four times more values between 6 to 8 than between 8 to 10.

The plot shows the specified cumulative distribution function (CDF) and the corresponding probability distribution function (PDF).

The piecewise linear CDF corresponds to a piecewise constant PDF.

Input Arguments

distname — Distribution name

'Uniform' | 'Normal' | 'Multinomial' | 'PiecewiseLinear' | 'Triangular'

Distribution name, specified as one of the following values:

Distribution Name	Description
'Uniform'	Uniform distribution — You specify the lower and upper bounds of the distribution.
'Normal'	Normal distribution — You specify the mean and standard deviation of the distribution.
'Multinomial'	Multinomial distribution — In a multinomial distribution, the outcome is one of 1, 2, ..., k. You specify the probability of each outcome, [p1,p2,..., pk]. The probabilities should sum to 1.
'PiecewiseLinear'	Piecewise Linear distribution — Use this distribution to make a custom distribution by specifying a piecewise linear cumulative distribution function (CDF). You specify the vector of values, x, at which the CDF changes slope and the corresponding vector of CDF values, Fx. The Fx value at any x is the probability of getting a value less than or equal to x. A piecewise linear CDF is created by linearly connecting the known CDF values, Fx. This piecewise linear CDF corresponds to a piecewise constant probability distribution function. For an example, see Specify Piecewise Linear Distribution Object.
'Triangular'	Triangular distribution — You specify the lower limit, peak location, and upper limit of the distribution.

For information about these distributions, see the Probability Distributions (Statistics and Machine Learning Toolbox) category.

Note

If you have Statistics and Machine Learning Toolbox software, you can use makedist to create objects for other distributions, such as the Gamma or Weibull distributions. For more information, see makedist (Statistics and Machine Learning Toolbox).

Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: makedist('Normal','mu',10) specifies a normal distribution with parameter mu equal to 10, and parameter sigma equal to the default value of 1.

Multinomial Distribution

Probabilities — Outcome probabilities

[0.500 0.500] (default) | vector of scalar values in the range [0,1]

Outcome probabilities for a multinomial distribution, specified as a vector of scalar values in the range [0,1]. The probabilities sum to 1 and correspond to outcomes [1, 2, ..., k], where k is the number of elements in the probabilities vector. This argument is valid only when distname is 'Multinomial'.

Example: 'Probabilities',[0.1 0.2 0.5 0.2] gives the probabilities that the outcome is 1, 2, 3, or 4, respectively.

Data Types: single | double

Normal Distribution

mu — Mean

0 (default) | scalar value

Mean of a normal distribution, specified as a scalar value. This argument is valid only when distname is 'Normal'.

Example: 'mu',2

Data Types: single | double

sigma — Standard deviation

1 (default) | nonnegative scalar value

Standard deviation of a normal distribution, specified as a nonnegative scalar value. This argument is valid only when distname is 'Normal'.

Example: 'sigma',2

Data Types: single | double

Piecewise Linear Distribution

x — Data values

1 (default) | monotonically increasing vector of scalar values

Data values at which the cumulative distribution function (cdf) changes slope for a piecewise linear distribution, specified as a monotonically increasing vector of scalar values. This argument is valid only when distname is 'PiecewiseLinear'.

Example: 'x',[1 2 3]

Data Types: single | double

Fx — cdf value at each value in x

1 (default) | monotonically increasing vector of scalar values that start at 0 and end at 1

cdf value at each value in x for a piecewise linear distribution, specified as a monotonically increasing vector of scalar values that start at 0 and end at 1. This argument is valid only when distname is 'PiecewiseLinear'.

Example: 'Fx',[0.2 0.5 1]

Data Types: single | double

Triangular Distribution

A — Lower limit

0 (default) | scalar value

Lower limit for a triangular distribution, specified as a scalar value. This argument is valid only when distname is 'Triangular'.

Example: 'A',-2

Data Types: single | double

B — Peak location

0.5 (default) | scalar value greater than or equal to A

Peak location for a triangular distribution, specified as a scalar value greater than or equal to A. This argument is valid only when distname is 'Triangular'.

Example: 'B',1

Data Types: single | double

C — Upper limit

1 (default) | scalar value greater than or equal to B

Upper limit for a triangular distribution, specified as a scalar value greater than or equal to B. This argument is valid only when distname is 'Triangular'.

Example: 'C',5

Data Types: single | double

Uniform Distribution

Lower — Lower limit

0 (default) | scalar value

Lower limit for a uniform distribution, specified as a scalar value. This argument is valid only when distname is 'Uniform'.

Example: 'Lower',-4

Data Types: single | double

Upper — Upper limit

1 (default) | scalar value greater than Lower

Upper limit for a uniform distribution, specified as a scalar value greater than Lower. This argument is valid only when distname is 'Uniform'.

Example: 'Upper',2

Data Types: single | double

Output Arguments

pd — Probability distribution

probability distribution object

Probability distribution, returned as a probability distribution object of the type specified by distname.

list — List of probability distributions

cell array of character vectors

List of probability distributions that makedist can create, returned as a cell array of character vectors.