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prob.LoglogisticDistribution class

Package: prob
Superclasses: prob.ToolboxFittableParametricDistribution

Loglogistic probability distribution object

Description

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

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

Input Arguments

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mu — Log mean0 (default) | positive scalar value

Log mean for the loglogistic distribution, specified as a positive scalar value.

Data Types: single | double

sigma — Log scale parameter1 (default) | positive scalar value

Log scale parameter for the loglogistic distribution, specified as a positive scalar value.

Data Types: single | double

Properties

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mu — Log meanpositive scalar value

Log mean for the loglogistic distribution, stored as a positive scalar value.

Data Types: single | double

sigma — Log scale parameterpositive scalar value

Log scale parameter for the loglogistic distribution, stored as a positive 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
icdfInverse cumulative distribution function of probability distribution object
iqrInterquartile range of probability distribution object
median Median of probability distribution object
pdfProbability density function of probability distribution object
randomGenerate random numbers from probability distribution object
truncateTruncate probability distribution object
meanMean of probability distribution object
negloglikNegative loglikelihood of probability distribution object
paramciConfidence intervals for probability distribution parameters
proflikProfile likelihood function for probability distribution object
std Standard deviation of probability distribution object
varVariance of probability distribution object

Definitions

Loglogistic Distribution

The loglogistic distribution is closely related to the logistic distribution. If x is distributed loglogistically with parameters μ and σ, then log(x) is distributed logistically with mean and standard deviation. This distribution is often used in survival analysis to model events that experience an initial rate increase, followed by a rate decrease.

The loglogistic distribution uses the following parameters.

ParameterDescriptionSupport
muLog mean
sigmaLog scale parameter

The probability density function (pdf) is

where .

Examples

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Create a Loglogistic Distribution Object Using Default Parameters

Create a loglogistic distribution object using the default parameter values.

pd = makedist('Loglogistic')
pd = 

  LoglogisticDistribution

  Log-Logistic distribution
       mu = 0
    sigma = 1

Create a Loglogistic Distribution Object Using Specified Parameters

Create a loglogistic distribution object by specifying the parameter values.

pd = makedist('Loglogistic','mu',5,'sigma',2)
pd = 

  LoglogisticDistribution

  Log-Logistic distribution
       mu = 5
    sigma = 2

Generate random numbers from the loglogistic distribution and compute their log values.

rng(19) % for reproducibility
x = random(pd,10000,1);
logx = log(x);

Compute the mean of the log values.

m = mean(logx)
m =

    4.9828

The mean of the log of x is equal to the mu parameter of x, since x has a loglogistic distribution.

Plot logx.

hist(logx,50)

The plot shows that the log values of x have a logistic distribution.

See Also

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