Statistics: LoglogisticDistribution

Class Definition: `LoglogisticDistribution`

statistics: LoglogisticDistribution

Log-logistic probability distribution object.

A LoglogisticDistribution object consists of parameters, a model description, and sample data for a log-logistic probability distribution.

The log-logistic distribution is a continuous probability distribution that models non-negative random variables whose logarithm follows the logistic distribution. It is defined by location parameter mu and scale parameter sigma.

There are several ways to create a LoglogisticDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the makedist function.
Use the constructor LoglogisticDistribution (mu, sigma) to create a log-logistic distribution with fixed parameter values mu and sigma.
Use the static method LoglogisticDistribution.fit (x, censor, freq, options) to fit a distribution to the data in x using the same input arguments as the loglfit function.

It is highly recommended to use fitdist and makedist functions to create probability distribution objects, instead of the class constructor or the aforementioned static method.

Further information about the log-logistic distribution can be found at https://en.wikipedia.org/wiki/Log-logistic_distribution

See also: fitdist, makedist, loglcdf, loglinv, loglpdf, loglrnd, loglfit, logllike, loglstat

Source Code: LoglogisticDistribution

Properties

A scalar value characterizing the mean of the logarithmic values of the log-logistic distribution. You can access the mu property using dot name assignment.

Example: 1


 ## Create a Log-logistic distribution with default parameters
 data = loglrnd (0, 1, 10000, 1);
 pd = fitdist (data, "Loglogistic");

 ## Query parameter 'mu' (mean of logarithmic values)
 pd.mu

 ## Set parameter 'mu'
 pd.mu = 1

 ## Use this to initialize or modify the mean of the logarithmic values in a
 ## Log-logistic distribution. The mu parameter must be a nonnegative real
 ## scalar, often representing the location in log-space for modeling
 ## positive skewed data like survival times or income distributions.

ans = 0.022913
pd =
  LoglogisticDistribution

  Log-Logistic distribution
       mu =        1
    sigma = 0.990419

Example: 2


 ## Create a Log-logistic distribution object by calling its constructor
 pd = LoglogisticDistribution (1.5, 2);

 ## Query parameter 'mu'
 pd.mu

 ## This demonstrates direct construction with a specific mu parameter,
 ## useful for modeling data with a known log-mean, such as in reliability
 ## engineering or financial modeling.

ans = 1.5000

A positive scalar value characterizing the scale of the logarithmic values of the log-logistic distribution. You can access the sigma property using dot name assignment.

Example: 1


 ## Create a Log-logistic distribution with default parameters
 data = loglrnd (0, 1, 10000, 1);
 pd = fitdist (data, "Loglogistic");

 ## Query parameter 'sigma' (scale of logarithmic values)
 pd.sigma

 ## Set parameter 'sigma'
 pd.sigma = 2

 ## Use this to initialize or modify the scale of the logarithmic values in a
 ## Log-logistic distribution. The sigma parameter must be a positive real
 ## scalar, controlling the shape and tail heaviness of the distribution.

ans = 0.9959
pd =
  LoglogisticDistribution

  Log-Logistic distribution
       mu = 0.00895226
    sigma =          2

Example: 2


 ## Create a Log-logistic distribution object by calling its constructor
 pd = LoglogisticDistribution (0, 1.5);

 ## Query parameter 'sigma'
 pd.sigma

 ## This shows how to set the sigma parameter directly via the constructor,
 ## ideal for modeling variability in positive skewed data, such as failure times.

ans = 1.5000

A character vector specifying the name of the probability distribution object. This property is read-only.

A scalar integer value specifying the number of parameters characterizing the probability distribution. This property is read-only.

A $2×1$ cell array of character vectors with each element containing the name of a distribution parameter. This property is read-only.

A $2×1$ cell array of character vectors with each element containing a short description of a distribution parameter. This property is read-only.

A $2×1$ numeric vector containing the values of the distribution parameters. This property is read-only. You can change the distribution parameters by assigning new values to the mu and sigma properties.

A $2×2$ numeric matrix containing the variance-covariance of the parameter estimates. Diagonal elements contain the variance of each estimated parameter, and non-diagonal elements contain the covariance between the parameter estimates. The covariance matrix is only meaningful when the distribution was fitted to data. If the distribution object was created with fixed parameters, or a parameter of a fitted distribution is modified, then all elements of the variance-covariance are zero. This property is read-only.

A $1×2$ logical vector specifying which parameters are fixed and which are estimated. true values correspond to fixed parameters, false values correspond to parameter estimates. This property is read-only.

A $1×2$ numeric vector specifying the truncation interval for the probability distribution. First element contains the lower boundary, second element contains the upper boundary. This property is read-only. You can only truncate a probability distribution with the truncate method.

A logical scalar value specifying whether a probability distribution is truncated or not. This property is read-only.

A scalar structure containing the following fields:

data: a numeric vector containing the data used for distribution fitting.
cens: a numeric vector of logical values indicating censoring information corresponding to the elements of the data used for distribution fitting. If no censoring vector was used for distribution fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values containing the frequency information corresponding to the elements of the data used for distribution fitting. If no frequency vector was used for distribution fitting, then this field defaults to an empty array.

Methods

LoglogisticDistribution: p = cdf (pd, x)
LoglogisticDistribution: p = cdf (pd, x, "upper")

p = cdf (pd, x) computes the CDF of the probability distribution object, pd, evaluated at the values in x.

p = cdf (…, "upper") returns the complement of the CDF of the probability distribution object, pd, evaluated at the values in x.

Example: 1


 ## Plot various CDFs from the Log-logistic distribution
 x = 0:0.01:10;
 data1 = loglrnd (0, 0.5, 10000, 1);
 data2 = loglrnd (0, 1, 10000, 1);
 data3 = loglrnd (0, 2, 10000, 1);
 pd1 = fitdist (data1, "Loglogistic");
 pd2 = fitdist (data2, "Loglogistic");
 pd3 = fitdist (data3, "Loglogistic");
 p1 = cdf (pd1, x);
 p2 = cdf (pd2, x);
 p3 = cdf (pd3, x);
 plot (x, p1, "-b", x, p2, "-g", x, p3, "-r")
 grid on
 legend ({"mu = 0, sigma = 0.5", "mu = 0, sigma = 1", "mu = 0, sigma = 2"}, ...
         "location", "southeast")
 title ("Log-logistic CDF")
 xlabel ("values in x (x > 0)")
 ylabel ("Cumulative probability")

 ## Use this to compute and visualize the cumulative distribution function
 ## for different Log-logistic distributions, showing how probability
 ## accumulates for positive values, useful in survival analysis or risk modeling.

LoglogisticDistribution: x = icdf (pd, p)

x = icdf (pd, p) computes the quantile (the inverse of the CDF) of the probability distribution object, pd, evaluated at the values in p.

Example: 1


 ## Plot various iCDFs from the Log-logistic distribution
 p = 0.0001:0.001:0.95;
 data1 = loglrnd (0, 0.5, 10000, 1);
 data2 = loglrnd (0, 1, 10000, 1);
 data3 = loglrnd (0, 2, 10000, 1);
 pd1 = fitdist (data1, "Loglogistic");
 pd2 = fitdist (data2, "Loglogistic");
 pd3 = fitdist (data3, "Loglogistic");
 x1 = icdf (pd1, p);
 x2 = icdf (pd2, p);
 x3 = icdf (pd3, p);
 plot (p, x1, "-b", p, x2, "-g", p, x3, "-r")
 grid on
 legend ({"mu = 0, sigma = 0.5", "mu = 0, sigma = 1", "mu = 0, sigma = 2"}, ...
         "location", "northwest")
 title ("Log-logistic iCDF")
 xlabel ("Probability")
 ylabel ("values in x (x > 0)")

 ## This demonstrates the inverse CDF (quantiles) for Log-logistic
 ## distributions, useful for finding values corresponding to given
 ## probabilities, such as percentiles in income data or survival quantiles.

LoglogisticDistribution: r = iqr (pd)

r = iqr (pd) computes the interquartile range of the probability distribution object, pd.

Example: 1


 ## Compute the interquartile range for a Log-logistic distribution
 data = loglrnd (0, 1, 10000, 1);
 pd = fitdist (data, "Loglogistic");
 iqr_value = iqr (pd)

 ## Use this to calculate the interquartile range, which measures the spread
 ## of the middle 50% of the distribution, helpful for understanding central
 ## variability in positive skewed data like lifetimes.

iqr_value = 2.7585

LoglogisticDistribution: m = mean (pd)

m = mean (pd) computes the mean of the probability distribution object, pd.

Example: 1


 ## Compute the mean for different Log-logistic distributions
 data1 = loglrnd (0, 0.5, 10000, 1);
 data2 = loglrnd (0, 1, 10000, 1);
 pd1 = fitdist (data1, "Loglogistic");
 pd2 = fitdist (data2, "Loglogistic");
 mean1 = mean (pd1)
 mean2 = mean (pd2)

 ## This shows how to compute the expected value for Log-logistic
 ## distributions with different sigma parameters. Note that the mean may be
 ## infinite for sigma <= 1, useful in heavy-tailed modeling.

mean1 = 1.5756
mean2 = Inf

LoglogisticDistribution: m = median (pd)

m = median (pd) computes the median of the probability distribution object, pd.

Example: 1


 ## Compute the median for different Log-logistic distributions
 data1 = loglrnd (0, 0.5, 10000, 1);
 data2 = loglrnd (0, 1, 10000, 1);
 pd1 = fitdist (data1, "Loglogistic");
 pd2 = fitdist (data2, "Loglogistic");
 median1 = median (pd1)
 median2 = median (pd2)

 ## Use this to find the median value, which splits the distribution
 ## into two equal probability halves, robust to the heavy tails in Log-logistic data.

median1 = 1.0142
median2 = 1.0243

LoglogisticDistribution: nlogL = negloglik (pd)

nlogL = negloglik (pd) computes the negative loglikelihood of the probability distribution object, pd.

Example: 1


 ## Compute the negative loglikelihood for a fitted Log-logistic distribution
 rand ("seed", 21);
 data = loglrnd (0, 1, 100, 1);
 pd_fitted = fitdist (data, "Loglogistic");
 nlogL = negloglik (pd_fitted)

 ## This is useful for assessing the fit of a Log-logistic distribution to
 ## data, with lower values indicating a better fit, often used in model
 ## selection or optimization.

nlogL = -187.83

LoglogisticDistribution: ci = paramci (pd)
LoglogisticDistribution: ci = paramci (pd, Name, Value)

ci = paramci (pd) computes the lower and upper boundaries of the 95% confidence interval for each parameter of the probability distribution object, pd.

ci = paramci (pd, Name, Value) computes the confidence intervals with additional options specified by Name-Value pair arguments listed below.

`Name`		`Value`
`"Alpha"`		A scalar value in the range $(0,1)$ specifying the significance level for the confidence interval. The default value 0.05 corresponds to a 95% confidence interval.
`"Parameter"`		A character vector or a cell array of character vectors specifying the parameter names for which to compute confidence intervals. By default, `paramci` computes confidence intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data, otherwise an empty array, [], is returned.

Example: 1


 ## Compute confidence intervals for parameters of a fitted Log-logistic
 ## distribution
 rand ("seed", 21);
 data = loglrnd (0, 1, 1000, 1);
 pd_fitted = fitdist (data, "Loglogistic");
 ci = paramci (pd_fitted, "Alpha", 0.05)

 ## Use this to obtain confidence intervals for the estimated parameters (mu
 ## and sigma), providing a range of plausible values given the data, especially
 ## useful in survival or reliability analysis.

ci =

  -0.061636   0.938148
   0.149957   1.041061

LoglogisticDistribution: y = pdf (pd, x)

y = pdf (pd, x) computes the PDF of the probability distribution object, pd, evaluated at the values in x.

Example: 1


 ## Plot various PDFs from the Log-logistic distribution
 x = 0:0.01:10;
 data1 = loglrnd (0, 0.5, 10000, 1);
 data2 = loglrnd (0, 1, 10000, 1);
 data3 = loglrnd (0, 2, 10000, 1);
 pd1 = fitdist (data1, "Loglogistic");
 pd2 = fitdist (data2, "Loglogistic");
 pd3 = fitdist (data3, "Loglogistic");
 y1 = pdf (pd1, x);
 y2 = pdf (pd2, x);
 y3 = pdf (pd3, x);
 plot (x, y1, "-b", x, y2, "-g", x, y3, "-r")
 grid on
 legend ({"mu = 0, sigma = 0.5", "mu = 0, sigma = 1", "mu = 0, sigma = 2"}, ...
         "location", "northeast")
 title ("Log-logistic PDF")
 xlabel ("values in x (x > 0)")
 ylabel ("Probability density")

 ## This visualizes the probability density function for Log-logistic
 ## distributions, showing the likelihood for positive values with varying tails.

LoglogisticDistribution: plot (pd)
LoglogisticDistribution: plot (pd, Name, Value)
LoglogisticDistribution: h = plot (…)

plot (pd) plots a probability density function (PDF) of the probability distribution object pd. If pd contains data, which have been fitted by fitdist, the PDF is superimposed over a histogram of the data.

plot (pd, Name, Value) specifies additional options with the Name-Value pair arguments listed below.

`Name`		`Value`
`"PlotType"`		A character vector specifying the plot type. `"pdf"` plots the probability density function (PDF). When `pd` is fit to data, the PDF is superimposed on a histogram of the data. `"cdf"` plots the cumulative density function (CDF). When `pd` is fit to data, the CDF is superimposed over an empirical CDF. `"probability"` plots a probability plot using a CDF of the data and a CDF of the fitted probability distribution. This option is available only when `pd` is fitted to data.
`"Discrete"`		A logical scalar to specify whether to plot the PDF or CDF of a discrete distribution object as a line plot or a stem plot, by specifying `false` or `true`, respectively. By default, it is `true` for discrete distributions and `false` for continuous distributions. When `pd` is a continuous distribution object, option is ignored.
`"Parent"`		An axes graphics object for plot. If not specified, the `plot` function plots into the current axes or creates a new axes object if one does not exist.

h = plot (…) returns a graphics handle to the plotted objects.

Example: 1


 ## Create a Log-logistic distribution with fixed parameters mu = 0 and
 ## sigma = 1 and plot its PDF.

 data = loglrnd (0, 1, 10000, 1);
 pd = fitdist (data, "Loglogistic");
 x = linspace (0.01, 20, 1000);
 y = pdf (pd, x);
 plot (x, y, "b", "LineWidth", 2)
 grid on
 title ("Fixed Log-logistic distribution with mu = 0 and sigma = 1")
 xlabel ("x")
 ylabel ("PDF")

Example: 2


 ## Generate a data set of 100 random samples from a Log-logistic
 ## distribution with parameters mu = 0 and sigma = 1. Fit a Log-logistic
 ## distribution to this data and plot its CDF superimposed over an empirical
 ## CDF.

 rand ("seed", 21);
 data = loglrnd (0, 1, 100, 1);
 pd_fitted = fitdist (data, "Loglogistic");
 ecdf (data);
 hold on;
 x = linspace (icdf (pd_fitted, 0.01), icdf (pd_fitted, 0.99), 1000);
 y = cdf (pd_fitted, x);
 plot (x, y, "r", "LineWidth", 2);
 txt = "Fitted Log-logistic distribution with mu = %0.2f and sigma = %0.2f";
 title (sprintf (txt, pd_fitted.mu, pd_fitted.sigma))
 legend ({"empirical CDF", "fitted CDF"}, "location", "southeast")
 xlabel ("x")
 ylabel ("CDF")
 grid on
 hold off;

 ## Use this to visualize the fitted CDF compared to the empirical CDF of the
 ## data, useful for assessing model fit in skewed positive data.

Example: 3


 ## Generate a data set of 200 random samples from a Log-logistic
 ## distribution with parameters mu = 0 and sigma = 1. Display a probability
 ## plot for the Log-logistic distribution fit to the data.

 rand ("seed", 21);
 data = loglrnd (0, 1, 200, 1);
 pd_fitted = fitdist (data, "Loglogistic");
 plot (pd_fitted, "PlotType", "probability")
 txt = strcat ("Probability plot of fitted Log-logistic", ...
               " distribution with mu = %0.2f and sigma = %0.2f");
 title (sprintf (txt, pd_fitted.mu, pd_fitted.sigma))
 legend ({"empirical CDF", "fitted CDF"}, "location", "southeast")

 ## This creates a probability plot to compare the fitted distribution to the
 ## data, useful for checking if the Log-logistic model captures the tail behavior.

LoglogisticDistribution: [nlogL, param] = proflik (pd, pnum)
LoglogisticDistribution: [nlogL, param] = proflik (pd, pnum, "Display", display)
LoglogisticDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
LoglogisticDistribution: [nlogL, param] = proflik (pd, pnum, setparam, "Display", display)

[nlogL, param] = proflik (pd, pnum) returns a vector nlogL of negative loglikelihood values and a vector param of corresponding parameter values for the parameter in the position indicated by pnum. By default, proflik uses the lower and upper bounds of the 95% confidence interval and computes 100 equispaced values for the selected parameter. pd must be fitted to data.

[nlogL, param] = proflik (pd, pnum, "Display", "on") also plots the profile likelihood against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum, setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum, setparam, "Display", "on") also plots the profile likelihood against the user-defined range of the selected parameter.

For the Log-logistic distribution, pnum = 1 selects the parameter mu and pnum = 2 selects the parameter sigma.

When opted to display the profile likelihood plot, proflik also plots the baseline loglikelihood computed at the lower bound of the 95% confidence interval and estimated maximum likelihood. The latter might not be observable if it is outside of the used-defined range of parameter values.

Example: 1


 ## Compute and plot the profile likelihood for the sigma parameter of a fitted
 ## Log-logistic distribution
 rand ("seed", 21);
 data = loglrnd (0, 1, 1000, 1);
 pd_fitted = fitdist (data, "Loglogistic");
 [nlogL, param] = proflik (pd_fitted, 2, "Display", "on");

 ## Use this to analyze the profile likelihood of the scale parameter (sigma),
 ## helping to understand the uncertainty and shape of the likelihood surface.

LoglogisticDistribution: r = random (pd)
LoglogisticDistribution: r = random (pd, rows)
LoglogisticDistribution: r = random (pd, rows, cols, …)
LoglogisticDistribution: r = random (pd, [sz])

r = random (pd) returns a random number from the distribution object pd.

When called with a single size argument, random returns a square matrix with the dimension specified. When called with more than one scalar argument, the first two arguments are taken as the number of rows and columns and any further arguments specify additional matrix dimensions. The size may also be specified with a row vector of dimensions, sz.

Example: 1


 ## Generate random samples from a Log-logistic distribution
 rand ("seed", 21);
 samples = loglrnd (0, 1, 500, 1);
 hist (samples, 50)
 p99 = prctile (samples, 99);
 xlim ([0, p99]);
 title ("Histogram of 500 random samples from Log-logistic(mu=0, sigma=1)")
 xlabel ("values in x (x > 0)")
 ylabel ("Frequency")

 ## This generates random samples from a Log-logistic distribution, useful
 ## for simulating positive skewed data like waiting times or economic variables.

LoglogisticDistribution: s = std (pd)

s = std (pd) computes the standard deviation of the probability distribution object, pd.

Example: 1


 ## Compute the standard deviation for a Log-logistic distribution
 data = loglrnd (0, 0.4, 10000, 1);
 pd = fitdist (data, "Loglogistic");
 std_value = std (pd)

 ## Use this to calculate the standard deviation, which measures the variability
 ## in the positive skewed values. Note it may be infinite for certain parameters.

std_value = 1.5927

LoglogisticDistribution: t = truncate (pd, lower, upper)

t = truncate (pd, lower, upper) returns a probability distribution t, which is the probability distribution pd truncated to the specified interval with lower limit, lower, and upper limit, upper. If pd is fitted to data with fitdist, the returned probability distribution t is not fitted, does not contain any data or estimated values, and it is as it has been created with the makedist function, but it includes the truncation interval.

Example: 1


 ## Plot the PDF of a Log-logistic distribution, with parameters mu = 0
 ## and sigma = 1, truncated at [0.5, 5] intervals. Generate 10000 random
 ## samples from this truncated distribution and superimpose a histogram scaled
 ## accordingly

 rand ("seed", 21);
 data_all = loglrnd (0, 1, 30000, 1);
 data = data_all(data_all >= 0.5 & data_all <= 5);
 data = data(1:10000);

 pd = fitdist (data, "Loglogistic");
 t = truncate (pd, 0.5, 5);

 [counts, centers] = hist (data, 50);
 bin_width = centers(2) - centers(1);
 bar (centers, counts / (sum (counts) * bin_width), 1);
 hold on;
 
 x = linspace (0.5, 5, 500);
 y = pdf (t, x);
 plot (x, y, "r", "linewidth", 2);
 title ("Log-logistic distribution (mu = 0, sigma = 1) truncated at [0.5, 5]")
 legend ("Truncated PDF", "Histogram")
 hold off;

 ## This demonstrates truncating a Log-logistic distribution to a specific
 ## range and visualizing the resulting distribution with random samples,
 ## useful for bounded positive data.

LoglogisticDistribution: v = var (pd)

v = var (pd) computes the variance of the probability distribution object, pd.

Example: 1


 ## Compute the variance for a Log-logistic distribution
 data = loglrnd (0, 0.4, 10000, 1);
 pd = fitdist (data, "Loglogistic");
 var_value = var (pd)

 ## Use this to calculate the variance, which quantifies the spread of the
 ## positive skewed values. Note it may be infinite for sigma <= 2.

var_value = 2.4054

Examples

 pd_fixed = makedist ("Loglogistic", "mu", 0, "sigma", 1)
 rand ("seed", 2);
 data = random (pd_fixed, 5000, 1);
 pd_fitted = fitdist (data, "Loglogistic")
 plot (pd_fitted)
 msg = "Fitted Log-logistic distribution with mu = %0.2f and sigma = %0.2f";
 title (sprintf (msg, pd_fitted.mu, pd_fitted.sigma))

pd_fixed =
  LoglogisticDistribution

  Log-Logistic distribution
       mu = 0
    sigma = 1

pd_fitted =
  LoglogisticDistribution

  Log-Logistic distribution
       mu = 0.0351959   [-0.0119722, 0.082364]
    sigma =  0.978072   [0.955719, 1.00095]

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Class Definition: LoglogisticDistribution

statistics: LoglogisticDistribution

Properties

mu

Example: 1

Example: 2

sigma

Example: 1

Example: 2

DistributionName

NumParameters

ParameterNames

ParameterDescription

ParameterValues

ParameterCovariance

ParameterIsFixed

Truncation

IsTruncated

InputData

Methods

cdf

LoglogisticDistribution: p = cdf (pd, x)

LoglogisticDistribution: p = cdf (pd, x, "upper")

Example: 1

icdf

LoglogisticDistribution: x = icdf (pd, p)

Example: 1

iqr

LoglogisticDistribution: r = iqr (pd)

Example: 1

mean

LoglogisticDistribution: m = mean (pd)

Example: 1

median

LoglogisticDistribution: m = median (pd)

Example: 1

negloglik

LoglogisticDistribution: nlogL = negloglik (pd)

Example: 1

paramci

Class Definition: `LoglogisticDistribution`

`mu`

`sigma`

`DistributionName`

`NumParameters`

`ParameterNames`

`ParameterDescription`

`ParameterValues`

`ParameterCovariance`

`ParameterIsFixed`

`Truncation`

`IsTruncated`

`InputData`

`cdf`

`LoglogisticDistribution: p = cdf (pd, x)`

`LoglogisticDistribution: p = cdf (pd, x, "upper")`

`icdf`

`LoglogisticDistribution: x = icdf (pd, p)`

`iqr`

`LoglogisticDistribution: r = iqr (pd)`

`mean`

`LoglogisticDistribution: m = mean (pd)`

`median`

`LoglogisticDistribution: m = median (pd)`

`negloglik`

`LoglogisticDistribution: nlogL = negloglik (pd)`

`paramci`

`LoglogisticDistribution: ci = paramci (pd)`

`LoglogisticDistribution: ci = paramci (pd, Name, Value)`

`pdf`

`LoglogisticDistribution: y = pdf (pd, x)`

`plot`

`LoglogisticDistribution: plot (pd)`

`LoglogisticDistribution: plot (pd, Name, Value)`

`LoglogisticDistribution: h = plot (…)`

`proflik`

`LoglogisticDistribution: [nlogL, param] = proflik (pd, pnum)`

`LoglogisticDistribution: [nlogL, param] = proflik (pd, pnum, "Display", display)`

`LoglogisticDistribution: [nlogL, param] = proflik (pd, pnum, setparam)`

`LoglogisticDistribution: [nlogL, param] = proflik (pd, pnum, setparam, "Display", display)`

`random`

`LoglogisticDistribution: r = random (pd)`

`LoglogisticDistribution: r = random (pd, rows)`

`LoglogisticDistribution: r = random (pd, rows, cols, …)`

`LoglogisticDistribution: r = random (pd, [sz])`

`std`

`LoglogisticDistribution: s = std (pd)`

`truncate`

`LoglogisticDistribution: t = truncate (pd, lower, upper)`

`var`

`LoglogisticDistribution: v = var (pd)`