Loglogistic probability distribution object
LoglogisticDistribution object consists of parameters, a
model description, and sample data for a loglogistic probability
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.
|Mean of logarithmic values|
|Scale parameter of logarithmic values|
There are several ways to create a
probability distribution object.
mu— Mean of logarithmic values
Mean of logarithmic values for the loglogistic distribution, specified as a positive scalar value.
sigma— Scale parameter of logarithmic values
Scale parameter of logarithmic values for the loglogistic distribution, specified as a positive scalar value.
|Cumulative distribution function|
|Inverse cumulative distribution function|
|Mean of probability distribution|
|Median of probability distribution|
|Negative loglikelihood of probability distribution|
|Confidence intervals for probability distribution parameters|
|Probability density function|
|Profile likelihood function for probability distribution|
|Standard deviation of probability distribution|
|Truncate probability distribution object|
|Variance of probability distribution|
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 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 has a loglogistic distribution.
The plot shows that the log values of
x have a logistic distribution.