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 a Normal Distribution Object

Create a normal distribution object using the default parameter values.

pd = makedist('Normal')

pd = 
  NormalDistribution

  Normal distribution
       mu = 0
    sigma = 1

Compute the interquartile range of the distribution.

r = iqr(pd)

r = 1.3490

Create a Gamma Distribution Object

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 a 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 a 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
'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 Pair 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

Example: 'a',3

Data Types: single | double

'b' — Second shape parameter

1 (default) | positive scalar value

Example: 'b',5

Data Types: single | double

Binomial Distribution

'N' — Number of trials

1 (default) | positive integer value

Example: 'N',25

Data Types: single | double

'p' — Probability of success

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

Example: 'p',0.25

Data Types: single | double

Birnbaum-Saunders Distribution

'beta' — Scale parameter

1 (default) | positive scalar value

Example: 'beta',2

Data Types: single | double

'gamma' — Shape parameter

1 (default) | nonnegative scalar value

Example: 'gamma',0

Data Types: single | double

Burr Distribution

'alpha' — Scale parameter

1 (default) | positive scalar value

Example: 'alpha',2

Data Types: single | double

'c' — First shape parameter

1 (default) | positive scalar value

Example: 'c',2

Data Types: single | double

'k' — Second shape parameter

1 (default) | positive scalar value

Example: 'k',5

Data Types: single | double

Exponential Distribution

'mu' — Mean parameter

1 (default) | positive scalar value

Example: 'mu',5

Data Types: single | double

Extreme Value Distribution

'mu' — Location parameter

0 (default) | scalar value

Example: 'mu',-2

Data Types: single | double

'sigma' — Scale parameter

1 (default) | nonnegative scalar value

Example: 'sigma',2

Data Types: single | double

Gamma Distribution

'a' — Shape parameter

1 (default) | positive scalar value

Example: 'a',2

Data Types: single | double

'b' — Scale parameter

1 (default) | nonnegative scalar value

Example: 'b',0

Data Types: single | double

Generalized Extreme Value Distribution

'k' — Shape parameter

0 (default) | scalar value

Example: 'k',0

Data Types: single | double

'sigma' — Scale parameter

1 (default) | nonnegative scalar value

Example: 'sigma',2

Data Types: single | double

'mu' — Location parameter

0 (default) | scalar value

Example: 'mu',1

Data Types: single | double

Generalized Pareto Distribution

'k' — Shape parameter

1 (default) | scalar value

Example: 'k',0

Data Types: single | double

'sigma' — Scale parameter

1 (default) | nonnegative scalar value

Example: 'sigma',2

Data Types: single | double

'theta' — Location parameter

1 (default) | scalar value

Example: 'theta',2

Data Types: single | double

Half–Normal Distribution

'mu' — Location parameter

0 (default) | scalar value

Example: 'mu',1

Data Types: single | double

'sigma' — Shape parameter

1 (default) | nonnegative scalar value

Example: 'sigma',2

Data Types: single | double

Inverse Gaussian Distribution

'mu' — Scale parameter

1 (default) | positive scalar value

Example: 'mu',2

Data Types: single | double

'lambda' — Shape parameter

1 (default) | positive scalar value

Example: 'lambda',4

Data Types: single | double

Logistic Distribution

'mu' — Mean

0 (default) | scalar value

Example: 'mu',2

Data Types: single | double

'sigma' — Scale parameter

1 (default) | nonnegative scalar value

Example: 'sigma',4

Data Types: single | double

Loglogistic Distribution

'mu' — Mean of logarithmic values

0 (default) | scalar value

Example: 'mu',2

Data Types: single | double

'sigma' — Scale parameter of logarithmic values

1 (default) | nonnegative scalar value

Example: 'sigma',4

Data Types: single | double

Lognormal Distribution

'mu' — Mean of logarithmic values

0 (default) | scalar value

Example: 'mu',2

Data Types: single | double

'sigma' — Standard deviation of logarithmic values

1 (default) | nonnegative scalar value

Example: 'sigma',2

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, 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.

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

Example: 'mu',5

Data Types: single | double

'omega' — Scale parameter

1 (default) | positive scalar value

Example: 'omega',5

Data Types: single | double

Negative Binomial Distribution

'R' — Number of successes

1 (default) | positive scalar value

Example: 'R',5

Data Types: single | double

'p' — Probability of success

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

Example: 'p',0.1

Data Types: single | double

Normal Distribution

'mu' — Mean

0 (default) | scalar value

Example: 'mu',2

Data Types: single | double

'sigma' — Standard deviation

1 (default) | nonnegative scalar value

Example: 'sigma',2

Data Types: single | double

Piecewise Linear Distribution

'x' — Data values

1 (default) | monotonically increasing vector of scalar values

Example: 'x',[1 2 3]

Data Types: single | double

'Fx' — cdf values

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

Example: 'Fx',[0.2 0.5 1]

Data Types: single | double

Poisson Distribution

'lambda' — Mean

1 (default) | nonnegative scalar value

Example: 'lambda',5

Data Types: single | double

Rayleigh Distribution

'b' — Defining parameter

1 (default) | positive scalar value

Example: 'b',3

Data Types: single | double

Rician Distribution

's' — Noncentrality parameter

1 (default) | nonnegative scalar value

Example: 's',0

Data Types: single | double

'sigma' — Scale parameter

1 (default) | positive scalar value

Example: 'sigma',2

Data Types: single | double

Stable Distribution

'alpha' — First shape parameter

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

Example: 'alpha',1

Data Types: single | double

'beta' — Second shape parameter

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

Example: 'beta',0.5

Data Types: single | double

'gam' — Scale parameter

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

Example: 'gam',2

Data Types: single | double

'delta' — Location parameter

0 (default) | scalar value

Example: 'delta',5

Data Types: single | double

t Location-Scale Distribution

'mu' — Location parameter

0 (default) | scalar value

Example: 'mu',-2

Data Types: single | double

'sigma' — Scale parameter

1 (default) | positive scalar value

Example: 'sigma',2

Data Types: single | double

'nu' — Degrees of freedom

5 (default) | positive scalar value

Example: 'nu',20

Data Types: single | double

Triangular Distribution

'a' — Lower limit

0 (default) | scalar value

Example: 'a',-2

Data Types: single | double

'b' — Peak location

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

Example: 'b',1

Data Types: single | double

'c' — Upper limit

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

Example: 'c',5

Data Types: single | double

Uniform Distribution

'lower' — Lower parameter

0 (default) | scalar value

Example: 'lower',-4

Data Types: single | double

'upper' — Upper parameter

1 (default) | scalar value greater than lower

Example: 'upper',2

Data Types: single | double

Weibull Distribution

'a' — Scale parameter

1 (default) | positive scalar value

Example: 'a',2

Data Types: single | double

'b' — Shape parameter

1 (default) | positive scalar value

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.