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BirnbaumSaundersDistribution

Birnbaum-Saunders probability distribution object

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Description

A BirnbaumSaundersDistribution object consists of parameters, a model description, and sample data for a Birnbaum-Saunders probability distribution.

The Birnbaum-Saunders distribution was originally proposed as a lifetime model for materials subject to cyclic patterns of stress and strain, where the ultimate failure of the material comes from the growth of a prominent flaw. In materials science, Miner's Rule suggests that the damage occurring after n cycles, at a stress level with an expected lifetime of N cycles, is proportional to n / N. Whenever Miner's Rule applies, the Birnbaum-Saunders model is a reasonable choice for a lifetime distribution model.

The Birnbaum-Saunders distribution uses the following parameters.

ParameterDescriptionSupport
betascale parameterβ > 0
gammashape parameterγ > 0

Creation

There are several ways to create a BirnbaumSaundersDistribution 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

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Distribution Parameters

Scale parameter of the Birnbaum-Saunders distribution, specified as a positive scalar value.

Data Types: single | double

Shape parameter of the Birnbaum-Saunders 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: 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: 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 of scalar values.

Data Types: single | double

This property is read-only.

Truncation interval for the probability distribution, specified as a vector of scalar values 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 function
gatherGather properties of Statistics and Machine Learning Toolbox object from GPU
icdfInverse cumulative distribution function
iqrInterquartile range of probability distribution
meanMean of probability distribution
medianMedian of probability distribution
negloglikNegative loglikelihood of probability distribution
paramciConfidence intervals for probability distribution parameters
pdfProbability density function
plotPlot probability distribution object
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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Open Live Script

Create a Birnbaum-Saunders distribution object using the default parameter values. 

pd = makedist('BirnbaumSaunders')
pd = 
  BirnbaumSaundersDistribution

  Birnbaum-Saunders distribution
     beta = 1
    gamma = 1
Open Live Script

Create a Birnbaum-Saunders distribution object by specifying the parameter values.

pd = makedist('BirnbaumSaunders','beta',2,'gamma',5)
pd = 
  BirnbaumSaundersDistribution

  Birnbaum-Saunders distribution
     beta = 2
    gamma = 5

Compute the mean of the distribution. 

m = mean(pd)
m = 
27

Extended Capabilities

Version History

Introduced in R2013a

See Also

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