Create probability distribution object
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Syntax
pd = makedist(distname)
pd = makedist(distname,Name,Value)
list = makedist
makedist -reset
Description
example
pd = makedist(distname) createsa probability distribution object for the distribution distname,using the default parameter values.
example
pd = makedist(distname,Name,Value) createsa probability distribution object with one or more distribution parametervalues specified by name-value pair arguments.
list = makedist returnsa cell array list containing a list of the probabilitydistributions that makedist can create.
makedist -reset resets the list of distributions by searching the path for files contained in a namespace 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
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Create Normal Distribution Object Using Default Parameter Values
Open Live Script
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 gather icdf iqr mean median negloglik paramci pdf plot proflik random std truncate var
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
Open Live Script
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
Open Live Script
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
Open Live Script
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
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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 pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose Name in quotes.
Example: makedist('Normal','mu',10) specifiesa normal distribution with parameter mu equal to10, and parameter sigma equal to the default valueof 1.
Beta Distribution
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Nakagami Distribution
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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
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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
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Piecewise Linear Distribution
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Poisson Distribution
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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
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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
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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
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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
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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
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Uniform Distribution
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Weibull Distribution
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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
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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.
Version History
Introduced in R2013a
See Also
fitdist | distributionFitter
Topics
- Working with Probability Distributions
- Supported Distributions
- Define Custom Distributions Using the Distribution Fitter App
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