# InverseGaussianDistribution

Inverse Gaussian probability distribution object

## Description

An InverseGaussianDistribution object consists of parameters, a model description, and sample data for an inverse Gaussian probability distribution.

Also known as the Wald distribution, the inverse Gaussian is used to model nonnegative positively skewed data. Inverse Gaussian distributions have many similarities to standard Gaussian (normal) distributions, which lead to applications in inferential statistics.

The inverse Gaussian distribution uses the following parameters.

ParameterDescriptionSupport
muScale parameter$\mu >0$
lambdaShape parameter$\lambda >0$

## Creation

There are several ways to create a InverseGaussianDistribution 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 for the inverse Gaussian distribution, specified as a positive scalar value.

Data Types: single | double

Shape parameter for the inverse Gaussian 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

 cdf Cumulative distribution function gather Gather properties of Statistics and Machine Learning Toolbox object 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 plot Plot probability distribution object 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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Create an inverse Gaussian distribution object using the default parameter values.

pd = makedist('InverseGaussian')
pd =
InverseGaussianDistribution

Inverse Gaussian distribution
mu = 1
lambda = 1

Create an inverse Gaussian distribution object by specifying parameter values.

pd = makedist('InverseGaussian','mu',2,'lambda',4)
pd =
InverseGaussianDistribution

Inverse Gaussian distribution
mu = 2
lambda = 4

Compute the standard deviation of the distribution.

s = std(pd)
s = 1.4142

## Version History

Introduced in R2013a