makedist

Create probability distribution object

Syntax

pd = makedist(distname)

pd = makedist(distname,Name,Value)

list = makedist

makedist -reset

Description

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

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.

makedist -reset resets the list of distributions by searching the path for files contained in a package named prob and implementing classes derived from ProbabilityDistribution. Use this syntax after you define a custom distribution function. For details, see Define Custom Distributions Using the Distribution Fitter App.

Examples

Create Normal Distribution Object Using Default Parameter Values

Create a normal distribution object using the default parameter values, which correspond to the parameters of the standard normal distribution.

pd = makedist('Normal')

pd = 
  NormalDistribution

  Normal distribution
       mu = 0
    sigma = 1

You can use the object functions of pd to evaluate the distribution and generate random numbers. Display the supported object functions.

methods(pd)

Methods for class prob.NormalDistribution:

cdf        iqr        negloglik  proflik    truncate   
gather     mean       paramci    random     var        
icdf       median     pdf        std        

For example, compute the interquartile range of the distribution by using the iqr function.

r = iqr(pd)

r = 1.3490

Create Gamma Distribution Object Using Default Parameter Values

Create a gamma distribution object using the default parameter values.

pd = makedist('Gamma')

pd = 
  GammaDistribution

  Gamma distribution
    a = 1
    b = 1

Compute the mean of the gamma distribution.

mean = mean(pd)

mean = 1

Specify Parameters for Normal Distribution Object

Create a normal distribution object with parameter values mu = 75 and sigma = 10.

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

pd = 
  NormalDistribution

  Normal distribution
       mu = 75
    sigma = 10

Specify Parameters for Gamma Distribution Object

Create a gamma distribution object with the parameter value a = 3 and the default value b = 1.

pd = makedist('Gamma','a',3)

pd = 
  GammaDistribution

  Gamma distribution
    a = 3
    b = 1

Input Arguments

distname — Distribution name

character vector | string scalar

Distribution name, specified as one of the following character vectors or string scalars. The distribution specified by distname determines the type of the returned probability distribution object.

Distribution Name	Description	Distribution Object
'Beta'	Beta distribution	BetaDistribution
'Binomial'	Binomial distribution	BinomialDistribution
'BirnbaumSaunders'	Birnbaum-Saunders distribution	BirnbaumSaundersDistribution
'Burr'	Burr distribution	BurrDistribution
'Exponential'	Exponential distribution	ExponentialDistribution
'ExtremeValue'	Extreme Value distribution	ExtremeValueDistribution
'Gamma'	Gamma distribution	GammaDistribution
'GeneralizedExtremeValue'	Generalized Extreme Value distribution	GeneralizedExtremeValueDistribution
'GeneralizedPareto'	Generalized Pareto distribution	GeneralizedParetoDistribution
'HalfNormal'	Half-normal distribution	HalfNormalDistribution
'InverseGaussian'	Inverse Gaussian distribution	InverseGaussianDistribution
'Logistic'	Logistic distribution	LogisticDistribution
'Loglogistic'	Loglogistic distribution	LoglogisticDistribution
'Lognormal'	Lognormal distribution	LognormalDistribution
'Loguniform'	Loguniform distribution	LoguniformDistribution
'Multinomial'	Multinomial distribution	MultinomialDistribution
'Nakagami'	Nakagami distribution	NakagamiDistribution
'NegativeBinomial'	Negative Binomial distribution	NegativeBinomialDistribution
'Normal'	Normal distribution	NormalDistribution
'PiecewiseLinear'	Piecewise Linear distribution	PiecewiseLinearDistribution
'Poisson'	Poisson distribution	PoissonDistribution
'Rayleigh'	Rayleigh distribution	RayleighDistribution
'Rician'	Rician distribution	RicianDistribution
'Stable'	Stable distribution	StableDistribution
'tLocationScale'	t Location-Scale distribution	tLocationScaleDistribution
'Triangular'	Triangular distribution	TriangularDistribution
'Uniform'	Uniform distribution	UniformDistribution
'Weibull'	Weibull distribution	WeibullDistribution

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.

Beta Distribution

a — First shape parameter

1 (default) | positive scalar value

First shape parameter of a beta distribution, specified as a positive scalar value. This argument is valid only when distname is 'Beta'.

Example: 'a',3

Data Types: single | double

b — Second shape parameter

1 (default) | positive scalar value

Second shape parameter of a beta distribution, specified as a positive scalar value. This argument is valid only when distname is 'Beta'.

Example: 'b',5

Data Types: single | double

Binomial Distribution

N — Number of trials

1 (default) | positive integer value

Number of trials for a binomial distribution, specified as a positive integer value. This argument is valid only when distname is 'Binomial'.

Example: 'N',25

Data Types: single | double

p — Probability of success

0.5 (default) | scalar value in the range [0,1]

Probability of success of any individual trial for a binomial distribution, specified as a scalar value in the range [0,1]. This argument is valid only when distname is 'Binomial'.

Example: 'p',0.25

Data Types: single | double

Birnbaum-Saunders Distribution

beta — Scale parameter

1 (default) | positive scalar value

Scale parameter of a Birnbaum-Saunders distribution, specified as a positive scalar value. This argument is valid only when distname is 'BirnbaumSaunders'.

Example: 'beta',2

Data Types: single | double

gamma — Shape parameter

1 (default) | positive scalar value

Shape parameter of a Birnbaum-Saunders distribution, specified as a positive scalar value. This argument is valid only when distname is 'BirnbaumSaunders'.

Example: 'gamma',0.5

Data Types: single | double

Burr Distribution

alpha — Scale parameter

1 (default) | positive scalar value

Scale parameter of a Burr distribution, specified as a positive scalar value. This argument is valid only when distname is 'Burr'.

Example: 'alpha',2

Data Types: single | double

c — First shape parameter

1 (default) | positive scalar value

First shape parameter of a Burr distribution, specified as a positive scalar value. This argument is valid only when distname is 'Burr'.

Example: 'c',2

Data Types: single | double

k — Second shape parameter

1 (default) | positive scalar value

Second shape parameter of a Burr distribution, specified as a positive scalar value. This argument is valid only when distname is 'Burr'.

Example: 'k',5

Data Types: single | double

Exponential Distribution

mu — Mean

1 (default) | positive scalar value

Mean of an exponential distribution, specified as a positive scalar value. This argument is valid only when distname is 'Exponential'.

Example: 'mu',5

Data Types: single | double

Extreme Value Distribution

mu — Location parameter

0 (default) | scalar value

Location parameter of an extreme value distribution, specified as a scalar value. This argument is valid only when distname is 'ExtremeValue'.

Example: 'mu',-2

Data Types: single | double

sigma — Scale parameter

1 (default) | nonnegative scalar value

Scale parameter of an extreme value distribution, specified as a nonnegative scalar value. This argument is valid only when distname is 'ExtremeValue'.

Example: 'sigma',2

Data Types: single | double

Gamma Distribution

a — Shape parameter

1 (default) | positive scalar value

Shape parameter of a gamma distribution, specified as a positive scalar value. This argument is valid only when distname is 'Gamma'.

Example: 'a',2

Data Types: single | double

b — Scale parameter

1 (default) | nonnegative scalar value

Scale parameter of a gamma distribution, specified as a nonnegative scalar value. This argument is valid only when distname is 'Gamma'.

Example: 'b',0

Data Types: single | double

Generalized Extreme Value Distribution

k — Shape parameter

0 (default) | scalar value

Shape parameter of a generalized extreme value distribution, specified as a scalar value. This argument is valid only when distname is 'GeneralizedExtremeValue'.

Example: 'k',0

Data Types: single | double

sigma — Scale parameter

1 (default) | nonnegative scalar value

Scale parameter of a generalized extreme value distribution, specified as a nonnegative scalar value. This argument is valid only when distname is 'GeneralizedExtremeValue'.

Example: 'sigma',2

Data Types: single | double

mu — Location parameter

0 (default) | scalar value

Location parameter of a generalized extreme value distribution, specified as a scalar value. This argument is valid only when distname is 'GeneralizedExtremeValue'.

Example: 'mu',1

Data Types: single | double

Generalized Pareto Distribution

k — Shape parameter

1 (default) | scalar value

Shape parameter of a generalized Pareto distribution, specified as a scalar value. This argument is valid only when distname is 'GeneralizedPareto'.

Example: 'k',0

Data Types: single | double

sigma — Scale parameter

1 (default) | nonnegative scalar value

Scale parameter of a generalized Pareto distribution, specified as a nonnegative scalar value. This argument is valid only when distname is 'GeneralizedPareto'.

Example: 'sigma',2

Data Types: single | double

theta — Location (threshold) parameter

1 (default) | scalar value

Location (threshold) parameter of a generalized Pareto distribution, specified as a scalar value. This argument is valid only when distname is 'GeneralizedPareto'.

Example: 'theta',2

Data Types: single | double

Half-Normal Distribution

mu — Location parameter

0 (default) | scalar value

Location parameter of a half-normal distribution, specified as a scalar value. This argument is valid only when distname is 'HalfNormal'.

Example: 'mu',1

Data Types: single | double

sigma — Scale parameter

1 (default) | nonnegative scalar value

Scale parameter of a half-normal distribution, specified as a nonnegative scalar value. This argument is valid only when distname is 'HalfNormal'.

Example: 'sigma',2

Data Types: single | double

Inverse Gaussian Distribution

mu — Scale parameter

1 (default) | positive scalar value

Scale parameter of an inverse Gaussian distribution, specified as a positive scalar value. This argument is valid only when distname is 'InverseGaussian'.

Example: 'mu',2

Data Types: single | double

lambda — Shape parameter

1 (default) | positive scalar value

Shape parameter of an inverse Gaussian distribution, specified as a positive scalar value. This argument is valid only when distname is 'InverseGaussian'.

Example: 'lambda',4

Data Types: single | double

Logistic Distribution

mu — Mean

0 (default) | scalar value

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

Example: 'mu',2

Data Types: single | double

sigma — Scale parameter

1 (default) | nonnegative scalar value

Scale parameter of a logistic distribution, specified as a nonnegative scalar value. This argument is valid only when distname is 'Logistic'.

Example: 'sigma',4

Data Types: single | double

Loglogistic Distribution

mu — Mean of logarithmic values

0 (default) | scalar value

Mean of logarithmic values for a loglogistic distribution, specified as a scalar value. This argument is valid only when distname is 'Loglogistic'.

Example: 'mu',2

Data Types: single | double

sigma — Scale parameter of logarithmic values

1 (default) | positive scalar value

Scale parameter of logarithmic values for a loglogistic distribution, specified as a positive scalar value. This argument is valid only when distname is 'Loglogistic'.

Example: 'sigma',4

Data Types: single | double

Lognormal Distribution

mu — Mean of logarithmic values

0 (default) | scalar value

Mean of logarithmic values for a lognormal distribution, specified as a scalar value. This argument is valid only when distname is 'Lognormal'.

Example: 'mu',2

Data Types: single | double

sigma — Standard deviation of logarithmic values

1 (default) | nonnegative scalar value

Standard deviation of logarithmic values for a lognormal distribution, specified as a nonnegative scalar value. This argument is valid only when distname is 'Lognormal'.

Example: 'sigma',2

Data Types: single | double

Loguniform Distribution

Lower — Lower limit

1 (default) | nonnegative scalar value

Lower limit for a loguniform distribution, specified as a nonnegative scalar value. This argument is valid only when distname is 'Loguniform'.

Example: 'Lower',2

Data Types: single | double

Upper — Upper limit

4 (default) | scalar value greater than Lower

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

Example: 'Upper',6

Data Types: single | double

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

Nakagami Distribution

mu — Shape parameter

1 (default) | positive scalar value

Shape parameter of a Nakagami distribution, specified as a positive scalar value. This argument is valid only when distname is 'Nakagami'.

Example: 'mu',5

Data Types: single | double

omega — Scale parameter

1 (default) | positive scalar value

Scale parameter of a Nakagami distribution, specified as a positive scalar value. This argument is valid only when distname is 'Nakagami'.

Example: 'omega',5

Data Types: single | double

Negative Binomial Distribution

R — Number of successes

1 (default) | positive scalar value

Number of successes for a negative binomial distribution, specified as a positive scalar value. This argument is valid only when distname is 'NegativeBinomial'.

Example: 'R',5

Data Types: single | double

P — Probability of success

0.5 (default) | scalar value in the range (0,1]

Probability of success of any individual trial for a negative binomial distribution, specified as a scalar value in the range (0,1]. This argument is valid only when distname is 'NegativeBinomial'.

Example: 'P',0.1

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

Poisson Distribution

lambda — Mean

1 (default) | nonnegative scalar value

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

Example: 'lambda',5

Data Types: single | double

Rayleigh Distribution

B — Defining parameter

1 (default) | positive scalar value

Defining parameter of a Rayleigh distribution, specified as a positive scalar value. This argument is valid only when distname is 'Rayleigh'.

Example: 'B',3

Data Types: single | double

Rician Distribution

s — Noncentrality parameter

1 (default) | nonnegative scalar value

Noncentrality parameter of a Rician distribution, specified as a nonnegative scalar value. This argument is valid only when distname is 'Rician'.

Example: 's',0

Data Types: single | double

sigma — Scale parameter

1 (default) | positive scalar value

Scale parameter of a Rician distribution, specified as a positive scalar value. This argument is valid only when distname is 'Rician'.

Example: 'sigma',2

Data Types: single | double

Stable Distribution

alpha — First shape parameter

2 (default) | scalar value in the range (0,2]

First shape parameter of a stable distribution, specified as a scalar value in the range (0,2]. This argument is valid only when distname is 'Stable'.

Example: 'alpha',1

Data Types: single | double

beta — Second shape parameter

0 (default) | scalar value in the range [–1,1]

Second shape parameter of a stable distribution, specified as a scalar value in the range [–1,1]. This argument is valid only when distname is 'Stable'.

Example: 'beta',0.5

Data Types: single | double

gam — Scale parameter

1 (default) | scalar value in the range (0,∞)

Scale parameter of a stable distribution, specified as a scalar value in the range (0,∞). This argument is valid only when distname is 'Stable'.

Example: 'gam',2

Data Types: single | double

delta — Location parameter

0 (default) | scalar value

Location parameter of a stable distribution, specified as a scalar value. This argument is valid only when distname is 'Stable'.

Example: 'delta',5

Data Types: single | double

t Location-Scale Distribution

mu — Location parameter

0 (default) | scalar value

Location parameter of a t location-scale distribution, specified as a scalar value. This argument is valid only when distname is 'tLocationScale'.

Example: 'mu',-2

Data Types: single | double

sigma — Scale parameter

1 (default) | positive scalar value

Scale parameter of a t location-scale distribution, specified as a positive scalar value. This argument is valid only when distname is 'tLocationScale'.

Example: 'sigma',2

Data Types: single | double

nu — Degrees of freedom

5 (default) | positive scalar value

Degrees of freedom of a t location-scale distribution, specified as a positive scalar value. This argument is valid only when distname is 'tLocationScale'.

Example: 'nu',20

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

Weibull Distribution

A — Scale parameter

1 (default) | positive scalar value

Scale parameter of a Weibull distribution, specified as a positive scalar value. This argument is valid only when distname is 'Weibull'.

Example: 'A',2

Data Types: single | double

B — Shape parameter

1 (default) | positive scalar value

Shape parameter of a Weibull distribution, specified as a positive scalar value. This argument is valid only when distname is 'Weibull'.

Example: 'B',5

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.

Alternative Functionality

App

The Distribution Fitter app opens a graphical user interface for you to import data from the workspace and interactively fit a probability distribution to that data. You can then save the distribution to the workspace as a probability distribution object. Open the Distribution Fitter app using distributionFitter, or click Distribution Fitter on the Apps tab.