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prob.GammaDistribution class

Package: prob
Superclasses: prob.ToolboxFittableParametricDistribution

Gamma probability distribution object

Description

prob.GammaDistribution is an object consisting of parameters, a model description, and sample data for a gamma probability distribution.

Create a probability distribution object with specified parameter values using makedist. Alternatively, fit a distribution to data using fitdist or the Distribution Fitting app.

Construction

pd = makedist('Gamma') creates a gamma probability distribution object using the default parameter values.

pd = makedist('Gamma','a',a,'b',b) creates a gamma probability distribution object using the specified parameter values.

Input Arguments

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Shape parameter for the gamma distribution, specified as a positive scalar value.

Data Types: single | double

Scale parameter for the gamma distribution, specified as a nonnegative scalar value.

Data Types: single | double

Properties

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Shape parameter for the gamma distribution, stored as a positive scalar value.

Data Types: single | double

Scale parameter for the gamma distribution, stored as a nonnegative scalar value.

Data Types: single | double

Probability distribution name, stored as a character vector. This property is read-only.

Data Types: char

Data used for distribution fitting, stored as a structure containing the following:

  • data: Data vector used for distribution fitting.

  • cens: Censoring vector, or empty if none.

  • freq: Frequency vector, or empty if none.

This property is read-only.

Data Types: struct

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.

Data Types: logical

Number of parameters for the probability distribution, stored as a positive integer value. This property is read-only.

Data Types: single | double

Covariance matrix of the parameter estimates, stored as a p-by-p matrix, where p is the number of parameters in the distribution. The (i,j) element is the covariance between the estimates of the ith parameter and the jth parameter. The (i,i) element is the estimated variance of the ith parameter. If parameter i is fixed rather than estimated by fitting the distribution to data, then the (i,i) elements of the covariance matrix are 0. This property is read-only.

Data Types: single | double

Distribution parameter descriptions, stored as a cell array of character vectors. Each cell contains a short description of one distribution parameter. This property is read-only.

Data Types: char

Logical flag for fixed parameters, stored as an array of logical values. If 0, the corresponding parameter in the ParameterNames array is not fixed. If 1, the corresponding parameter in the ParameterNames array is fixed. This property is read-only.

Data Types: logical

Distribution parameter names, stored as a cell array of character vectors. This property is read-only.

Data Types: char

Distribution parameter values, stored as a vector. This property is read-only.

Data Types: single | double

Truncation interval for the probability distribution, stored as a vector containing the lower and upper truncation boundaries. This property is read-only.

Data Types: single | double

Methods

Inherited Methods

cdf Cumulative distribution function of probability distribution object
icdfInverse cumulative distribution function of probability distribution object
iqrInterquartile range of probability distribution object
median Median of probability distribution object
pdfProbability density function of probability distribution object
randomGenerate random numbers from probability distribution object
truncateTruncate probability distribution object
meanMean of probability distribution object
negloglikNegative log likelihood of probability distribution object
paramciConfidence intervals for probability distribution parameters
proflikProfile likelihood function for probability distribution object
std Standard deviation of probability distribution object
varVariance of probability distribution object

Definitions

Gamma Distribution

The gamma distribution is a two-parameter family of distributions used to model sums of exponentially distributed random variables. The chi-square and the exponential distributions, which are children of the gamma distribution, are one-parameter distributions that fix one of the two gamma parameters.

The gamma distribution uses the following parameters.

ParameterDescriptionSupport
aShape parametera>0
bScale parameterb0

The probability density function (pdf) is

f(x|a,b)=1baΓ(a)xa1exb;x>0,

where Γ() is the Gamma function.

Examples

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Create a gamma distribution object using the default parameter values.

pd = makedist('Gamma')
pd = 

  GammaDistribution

  Gamma distribution
    a = 1
    b = 1

Create a gamma distribution object by specifying the parameter values.

pd = makedist('Gamma', 'a',2,'b',4)
pd = 

  GammaDistribution

  Gamma distribution
    a = 2
    b = 4

Compute the mean of the distribution.

m = mean(pd)
m =

     8
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