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BirnbaumSaundersDistribution

Birnbaum-Saunders probability distribution object

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Description

ABirnbaumSaundersDistributionobject 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 afterncycles, at a stress level with an expected lifetime ofNcycles, is proportional ton/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.

Parameter Description 万博1manbetx
beta scale parameter β> 0
gamma shape parameter γ> 0

Creation

There are several ways to create aBirnbaumSaundersDistributionprobability distribution object.

  • Create a distribution with specified parameter values usingmakedist.

  • Fit a distribution to data usingfitdist.

  • Interactively fit a distribution to data using theDistribution Fitter应用程序。

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. IfIsTruncatedequals0, the distribution is not truncated. IfIsTruncatedequals1, 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 ap-by-pmatrix, wherepis the number of parameters in the distribution. The (i,j) element is the covariance between the estimates of theith parameter and thejth parameter. The (i,i) element is the estimated variance of theith parameter. If parameteriis 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. If0, the corresponding parameter in theParameterNamesarray is not fixed. If1, the corresponding parameter in theParameterNamesarray 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.

数据用于分布拟合,指定为一个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.

分布参数名称,指定as a cell array of character vectors.

Data Types:char

Object Functions

cdf Cumulative distribution function
gather Gather properties ofStatistics and Machine Learning Toolboxobject from GPU
icdf Inverse cumulative distribution function
iqr Interquartile range of probability distribution
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative loglikelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density function
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance 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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