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prob.LogisticDistribution class

Package: prob
Superclasses: prob.ToolboxFittableParametricDistribution

Logistic probability distribution object

Description

prob.LogisticDistribution is an object consisting of parameters, a model description, and sample data for a logistic 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('Logistic') creates a logistic probability distribution object using the default parameter values.

pd = makedist('Logistic','mu',mu,'sigma',sigma) creates a logistic probability distribution object using the specified parameter values.

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mu — Mean0 (default) | scalar value

Mean of the logistic distribution, specified as a scalar value.

Data Types: single | double

sigma — Scale parameter1 (default) | nonnegative scalar value

Scale parameter of the logistic distribution, specified as a nonnegative scalar value.

Data Types: single | double

Properties

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mu — Meanscalar value

Mean of the logistic distribution, stored as a scalar value.

Data Types: single | double

sigma — Scale parameternonnegative scalar value

Scale parameter of the logistic distribution, stored as a nonnegative scalar value.

Data Types: single | double

DistributionName — Probability distribution nameprobability distribution name string

Probability distribution name, stored as a valid probability distribution name string. This property is read-only.

Data Types: char

InputData — Data used for distribution fittingstructure

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

IsTruncated — Logical flag for truncated distribution0 | 1

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

NumParameters — Number of parameterspositive integer value

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

Data Types: single | double

ParameterCovariance — Covariance matrix of the parameter estimatesmatrix of scalar values

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

ParameterDescription — Distribution parameter descriptionscell array of strings

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

Data Types: char

ParameterIsFixed — Logical flag for fixed parametersarray of logical values

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

ParameterNames — Distribution parameter namescell array of strings

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

Data Types: char

ParameterValues — Distribution parameter valuesvector of scalar values

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

Data Types: single | double

Truncation — Truncation intervalvector of scalar values

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 icdf Inverse cumulative distribution function of probability distribution object iqr Interquartile range of probability distribution object median Median of probability distribution object pdf Probability density function of probability distribution object random Generate random numbers from probability distribution object truncate Truncate probability distribution object
 mean Mean of probability distribution object negloglik Negative loglikelihood of probability distribution object paramci Confidence intervals for probability distribution parameters proflik Profile likelihood function for probability distribution object std Standard deviation of probability distribution object var Variance of probability distribution object

Definitions

Logistic Distribution

The logistic distribution is used for growth models and in logistic regression. It has longer tails and a higher kurtosis than the normal distribution.

The logistic distribution uses the following parameters.

ParameterDescriptionSupport
muMean$-\infty <\mu <\infty$
sigmaScale parameter$\sigma \ge 0$

The probability density function (pdf) is

$f\left(x|\mu ,\sigma \right)=\frac{\mathrm{exp}\left\{\frac{x-\mu }{\sigma }\right\}}{\sigma {\left(1+\mathrm{exp}\left\{\frac{x-\mu }{\sigma }\right\}\right)}^{2}}\text{ };\text{ }-\infty

Examples

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Create a Logistic Distribution Object Using Default Parameters

Create a logistic distribution object using the default parameter values.

`pd = makedist('Logistic')`
```pd =

LogisticDistribution

Logistic distribution
mu = 0
sigma = 1```

Create a Logistic Distribution Object Using Specified Parameters

Create a logistic distribution object by specifying parameter values.

`pd = makedist('Logistic', 'mu',2,'sigma',4)`
```pd =

LogisticDistribution

Logistic distribution
mu = 2
sigma = 4```

Compute the standard deviation of the distribution.

`s = std(pd)`
```s =

7.2552```