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tLocationScaleDistribution

t Location-Scale probability distribution object

Description

A tLocationScaleDistribution object consists of parameters, a model description, and sample data for a t location-scale probability distribution.

The t location-scale distribution is useful for modeling data distributions with heavier tails (more prone to outliers) than the normal distribution. It approaches the normal distribution as ν approaches infinity, and smaller values of ν yield heavier tails.

The t location-scale distribution uses the following parameters.

ParameterDescriptionSupport
muLocation parameter<μ<
sigmaScale parameterσ>0
nuShape parameterν>0

Creation

There are several ways to create a tLocationScaleDistribution probability distribution object.

  • Create a distribution with specified parameter values using makedist.

  • Fit a distribution to data using fitdist.

  • Interactively fit a distribution to data using the Distribution Fitter app.

Properties

expand all

Distribution Parameters

Location parameter of the t location-scale distribution, specified as a scalar value.

Data Types: single | double

Scale parameter of the t location-scale distribution, specified as a positive scalar value.

Data Types: single | double

Degrees of freedom of the t location-scale distribution, specified as a positive scalar value.

Data Types: single | double

Distribution Characteristics

This property is read-only.

Logical flag for truncated distribution, specified as a logical value. If IsTruncated equals 0, the distribution is not truncated. If IsTruncated equals 1, the distribution is truncated.

Data Types: logical

This property is read-only.

Number of parameters for the probability distribution, specified as a positive integer value.

Data Types: single | double

This property is read-only.

Covariance matrix of the parameter estimates, specified 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.

Data Types: single | double

This property is read-only.

Logical flag for fixed parameters, specified 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.

Data Types: logical

This property is read-only.

Distribution parameter values, specified as a vector.

Data Types: single | double

This property is read-only.

Truncation interval for the probability distribution, specified as a vector containing the lower and upper truncation boundaries.

Data Types: single | double

Other Object Properties

This property is read-only.

Probability distribution name, specified as a character vector.

Data Types: char

This property is read-only.

Data used for distribution fitting, specified 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.

Data Types: struct

This property is read-only.

Distribution parameter descriptions, specified as a cell array of character vectors. Each cell contains a short description of one distribution parameter.

Data Types: char

This property is read-only.

Distribution parameter names, specified as a cell array of character vectors.

Data Types: char

Object Functions

cdfCumulative distribution functions
icdfInverse cumulative distribution functions
iqrInterquartile range
meanMean of probability distribution
medianMedian of probability distribution
negloglikNegative log likelihood of probability distribution
paramciConfidence intervals for probability distribution parameters
pdfProbability density functions
proflikProfile likelihood function for probability distribution
randomRandom numbers
stdStandard deviation of probability distribution
truncateTruncate probability distribution object
varVariance of probability distribution

Examples

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Create a location scale distribution object using the default parameter values.

pd = makedist('tLocationScale')
pd = 

  tLocationScaleDistribution

  t Location-Scale distribution
       mu = 0
    sigma = 1
       nu = 5

Create a location-scale distribution object by specifying the parameter values.

pd = makedist('tLocationScale','mu',-2,'sigma',1,'nu',20)
pd = 

  tLocationScaleDistribution

  t Location-Scale distribution
       mu = -2
    sigma =  1
       nu = 20

Compute the interquartile range of the distribution.

r = iqr(pd)
r =

    1.3739

Introduced in R2013a

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