Statistics: tLocationScaleDistribution

Class Definition: `tLocationScaleDistribution`

statistics: tLocationScaleDistribution

Location-Scale Student’s T probability distribution object.

A tLocationScaleDistribution object consists of parameters, a model description, and sample data for a location-scale Student’s T probability distribution.

The location-scale Student’s T distribution is a continuous probability distribution that generalizes the standard Student’s T distribution by including location and scale parameters. It is defined by location parameter mu, scale parameter sigma, and degrees of freedom nu.

There are several ways to create a tLocationScaleDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the makedist function.
Use the constructor tLocationScaleDistribution (mu, sigma, nu) to create a location-scale Student’s T distribution with fixed parameter values mu, sigma, and nu.
Use the static method tLocationScaleDistribution.fit (x, censor, freq, options) to fit a distribution to the data in x using the same input arguments as the tlsfit 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 location-scale Student’s T distribution can be found at https://en.wikipedia.org/wiki/Student%27s_t-distribution#Location-scale_t_distribution

See also: fitdist, makedist, tlscdf, tlsinv, tlspdf, tlsrnd, tlsfit, tlslike, tlsstat

Source Code: tLocationScaleDistribution

Properties

A scalar value characterizing the location of the location-scale Student’s T distribution. You can access the mu property using dot name assignment.

Example: 1


 ## Create a t Location-Scale distribution by fitting to data
 data = tlsrnd (0, 1, 5, 10000, 1);  % Generate data with mu=0, sigma=1, nu=5
 pd = fitdist (data, "tLocationScale");

 ## Query parameter 'mu' (location parameter)
 pd.mu

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

 ## Use this to initialize or modify the location parameter of a t Location-Scale
 ## distribution. The location parameter (mu) is a real scalar that shifts the
 ## distribution, useful for modeling data centered around a specific value.

ans = -8.6155e-03
pd =
  tLocationScaleDistribution

  t Location-Scale distribution
       mu =       1
    sigma = 1.01003
       nu = 5.40008

Example: 2


 ## Create a t Location-Scale distribution object by calling its constructor
 pd = tLocationScaleDistribution (2, 1, 5);

 ## Query parameter 'mu'
 pd.mu

 ## This demonstrates direct construction with a specific location parameter,
 ## ideal for modeling data with a known center, such as test scores or residuals.

ans = 2

A positive scalar value characterizing the scale of the location-scale Student’s T distribution. You can access the sigma property using dot name assignment.

Example: 1


 ## Create a t Location-Scale distribution with fitted parameters
 data = tlsrnd (0, 1, 5, 10000, 1);  % Generate data with mu=0, sigma=1, nu=5
 pd = fitdist (data, "tLocationScale");

 ## Query parameter 'sigma' (scale parameter)
 pd.sigma

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

 ## Use this to initialize or modify the scale parameter, which controls the
 ## spread of the t Location-Scale distribution. Sigma must be a positive real
 ## scalar, useful for modeling variability in data like financial returns.

ans = 0.9967
pd =
  tLocationScaleDistribution

  t Location-Scale distribution
       mu = -0.0162831
    sigma =          2
       nu =    5.29942

Example: 2


 ## Create a t Location-Scale distribution object by calling its constructor
 pd = tLocationScaleDistribution (0, 1.5, 5);

 ## Query parameter 'sigma'
 pd.sigma

 ## This shows how to set the scale parameter directly via the constructor,
 ## useful for modeling data with specific variability, such as process errors.

ans = 1.5000

A positive scalar value characterizing the degrees of freedom of the location-scale Student’s T distribution. You can access the nu property using dot name assignment.

Example: 1


 ## Create a t Location-Scale distribution with fitted parameters
 data = tlsrnd (0, 1, 5, 10000, 1);  % Generate data with mu=0, sigma=1, nu=5
 pd = fitdist (data, "tLocationScale");

 ## Query parameter 'nu' (degrees of freedom)
 pd.nu

 ## Set parameter 'nu'
 pd.nu = 10

 ## Use this to initialize or modify the degrees of freedom, which controls the
 ## tail heaviness of the t Location-Scale distribution. Nu must be a positive
 ## real scalar, useful for modeling heavy-tailed data like stock returns.

ans = 4.9211
pd =
  tLocationScaleDistribution

  t Location-Scale distribution
       mu = 0.0128332
    sigma =   1.00553
       nu =        10

Example: 2


 ## Create a t Location-Scale distribution object by calling its constructor
 pd = tLocationScaleDistribution (0, 1, 3);

 ## Query parameter 'nu'
 pd.nu

 ## This demonstrates setting the degrees of freedom directly via the constructor,
 ## ideal for modeling data with specific tail behavior, such as outlier-prone datasets.

ans = 3

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 $3×1$ cell array of character vectors with each element containing the name of a distribution parameter. This property is read-only.

A $3×1$ cell array of character vectors with each element containing a short description of a distribution parameter. This property is read-only.

A $3×1$ 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, sigma, and nu properties.

A $3×3$ 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 $1×3$ 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

tLocationScaleDistribution: p = cdf (pd, x)
tLocationScaleDistribution: 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 t Location-Scale distribution
 x = -5:0.01:5;
 data1 = tlsrnd (0, 0.5, 5, 10000, 1);
 data2 = tlsrnd (0, 1, 5, 10000, 1);
 data3 = tlsrnd (0, 2, 5, 10000, 1);
 pd1 = fitdist (data1, "tLocationScale");
 pd2 = fitdist (data2, "tLocationScale");
 pd3 = fitdist (data3, "tLocationScale");
 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, nu = 5", "mu = 0, sigma = 1, nu = 5", ...
         "mu = 0, sigma = 2, nu = 5"}, "location", "southeast")
 title ("t Location-Scale CDF")
 xlabel ("Values in x")
 ylabel ("Cumulative probability")

 ## Use this to compute and visualize the cumulative distribution function
 ## for different t Location-Scale distributions, showing how probability
 ## accumulates, useful in risk analysis or hypothesis testing.

tLocationScaleDistribution: 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 t Location-Scale distribution
 p = 0.001:0.001:0.999;
 data1 = tlsrnd (0, 0.5, 5, 10000, 1);
 data2 = tlsrnd (0, 1, 5, 10000, 1);
 data3 = tlsrnd (0, 2, 5, 10000, 1);
 pd1 = fitdist (data1, "tLocationScale");
 pd2 = fitdist (data2, "tLocationScale");
 pd3 = fitdist (data3, "tLocationScale");
 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, nu = 5", "mu = 0, sigma = 1, nu = 5", ...
         "mu = 0, sigma = 2, nu = 5"}, "location", "northwest")
 title ("t Location-Scale iCDF")
 xlabel ("Probability")
 ylabel ("Values in x")

 ## This demonstrates the inverse CDF (quantiles) for t Location-Scale
 ## distributions, useful for finding critical values or thresholds in statistical testing.

tLocationScaleDistribution: r = iqr (pd)

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

Example: 1


 ## Compute the interquartile range for a t Location-Scale distribution
 data = tlsrnd (0, 1, 5, 10000, 1);
 pd = fitdist (data, "tLocationScale");
 iqr_value = iqr (pd)

 ## Use this to calculate the interquartile range, which measures the spread
 ## of the middle 50% of the distribution, helpful for assessing central variability.

iqr_value = 1.4477

tLocationScaleDistribution: m = mean (pd)

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

Example: 1


 ## Compute the mean for different t Location-Scale distributions
 data1 = tlsrnd (0, 0.5, 5, 10000, 1);
 data2 = tlsrnd (0, 1, 5, 10000, 1);
 pd1 = fitdist (data1, "tLocationScale");
 pd2 = fitdist (data2, "tLocationScale");
 mean1 = mean (pd1)
 mean2 = mean (pd2)

 ## This shows how to compute the expected value for t Location-Scale
 ## distributions, representing the average value, useful in financial modeling or quality control.

mean1 = -1.1782e-04
mean2 = -0.015206

tLocationScaleDistribution: m = median (pd)

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

Example: 1


 ## Compute the median for different t Location-Scale distributions
 data1 = tlsrnd (0, 0.5, 5, 10000, 1);
 data2 = tlsrnd (0, 1, 5, 10000, 1);
 pd1 = fitdist (data1, "tLocationScale");
 pd2 = fitdist (data2, "tLocationScale");
 median1 = median (pd1)
 median2 = median (pd2)

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

median1 = 4.4011e-04
median2 = 0.018577

tLocationScaleDistribution: 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 t Location-Scale distribution
 rand ("seed", 21);
 data = tlsrnd (0, 1, 5, 100, 1);
 pd_fitted = fitdist (data, "tLocationScale");
 params = [pd_fitted.mu, pd_fitted.sigma, pd_fitted.nu];
 nlogL_tlslike = tlslike (params, data)

 ## This is useful for assessing the fit of a t Location-Scale distribution to
 ## data, with lower values indicating a better fit, often used in model comparison.

nlogL_tlslike = 171.08

tLocationScaleDistribution: ci = paramci (pd)
tLocationScaleDistribution: 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 t Location-Scale
 ## distribution
 rand ("seed", 21);
 data = tlsrnd (0, 1, 5, 1000, 1);
 pd_fitted = fitdist (data, "tLocationScale");
 ci = paramci (pd_fitted, "Alpha", 0.05)

 ## Use this to obtain confidence intervals for the estimated parameters (mu,
 ## sigma, nu), providing a range of plausible values given the data.

ci =

  -6.0005e-02   1.0178e+00   5.1018e+00
   8.9910e-02   1.1804e+00   1.3766e+01

tLocationScaleDistribution: 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 t Location-Scale distribution
 x = -5:0.01:5;
 data1 = tlsrnd (0, 0.5, 5, 10000, 1);
 data2 = tlsrnd (0, 1, 5, 10000, 1);
 data3 = tlsrnd (0, 2, 5, 10000, 1);
 pd1 = fitdist (data1, "tLocationScale");
 pd2 = fitdist (data2, "tLocationScale");
 pd3 = fitdist (data3, "tLocationScale");
 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, nu = 5", "mu = 0, sigma = 1, nu = 5", ...
         "mu = 0, sigma = 2, nu = 5"}, "location", "northeast")
 title ("t Location-Scale PDF")
 xlabel ("Values in x")
 ylabel ("Probability density")

 ## This visualizes the probability density function for t Location-Scale
 ## distributions, showing the likelihood across values, useful for data analysis.

tLocationScaleDistribution: plot (pd)
tLocationScaleDistribution: plot (pd, Name, Value)
tLocationScaleDistribution: 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 t Location-Scale distribution with fixed parameters and plot its PDF
 pd = tLocationScaleDistribution (0, 1, 5);
 plot (pd)
 title ("t Location-Scale distribution with mu = 0, sigma = 1, nu = 5")

 ## Use this to visualize the PDF of a t Location-Scale distribution with
 ## fixed parameters, helpful for theoretical exploration.

Example: 2


 ## Generate a data set and plot the CDF of a fitted t Location-Scale distribution
 rand ("seed", 21);
 data = tlsrnd (0, 1, 5, 100, 1);
 pd_fitted = fitdist (data, "tLocationScale");
 plot (pd_fitted, "PlotType", "cdf")
 txt = "Fitted t Location-Scale distribution with mu = %0.2f, sigma = %0.2f, nu = %0.2f";
 title (sprintf (txt, pd_fitted.mu, pd_fitted.sigma, pd_fitted.nu))
 legend ({"empirical CDF", "fitted CDF"}, "location", "southeast")

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

Example: 3


 ## Generate a data set and display a probability plot for a fitted t Location-Scale distribution
 rand ("seed", 21);
 data = tlsrnd (0, 1, 5, 200, 1);
 pd_fitted = fitdist (data, "tLocationScale");
 plot (pd_fitted, "PlotType", "probability")
 txt = strcat ("Probability plot of fitted t Location-Scale", ...
               " distribution with mu = %0.2f, sigma = %0.2f, nu = %0.2f");
 title (sprintf (txt, pd_fitted.mu, pd_fitted.sigma, pd_fitted.nu))
 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 t Location-Scale model is appropriate.

tLocationScaleDistribution: [nlogL, param] = proflik (pd, pnum)
tLocationScaleDistribution: [nlogL, param] = proflik (pd, pnum, "Display", display)
tLocationScaleDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
tLocationScaleDistribution: [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 location-scale Student’s T distribution, pnum = 1 selects the parameter mu, pnum = 2 selects the parameter sigma, and pnum = 3 selects the parameter nu.

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 scale parameter
 rand ("seed", 21);
 data = tlsrnd (0, 1, 5, 1000, 1);
 pd_fitted = fitdist (data, "tLocationScale");
 [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 in parameter estimates.

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

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

When called with a single size argument, tlsrnd 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 t Location-Scale distribution
 rand ("seed", 21);
 samples = tlsrnd (0, 1, 5, 500, 1);
 hist (samples, 50)
 title ("Histogram of 500 random samples from t Location-Scale(mu=0, sigma=1, nu=5)")
 xlabel ("Values in x")
 ylabel ("Frequency")

 ## This generates random samples from a t Location-Scale distribution, useful
 ## for simulating data with heavy tails, such as financial or experimental data.

tLocationScaleDistribution: s = std (pd)

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

Example: 1


 ## Compute the standard deviation for a t Location-Scale distribution
 data = tlsrnd (0, 1, 5, 10000, 1);
 pd = fitdist (data, "tLocationScale");
 std_value = std (pd)

 ## Use this to calculate the standard deviation, which measures the variability
 ## in the distribution, useful for understanding data dispersion.

std_value = 1.2839

tLocationScaleDistribution: 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 truncated t Location-Scale distribution
 rand ("seed", 21);
 data_all = tlsrnd (0, 1, 5, 20000, 1);
 data = data_all(data_all >= -1 & data_all <= 1);
 data = data(1:10000);

 pd = fitdist (data, "tLocationScale");
 t = truncate (pd, -1, 1);

 [counts, centers] = hist (data, 50);
 bin_width = centers(2) - centers(1);
 bar (centers, counts / (sum (counts) * bin_width), 1);
 hold on;

 ## Plot histogram and truncated PDF
 x = linspace (0.5, 5, 500);
 y = pdf (t, x);
 plot (x, y, "r", "linewidth", 2);
 title ("t Location-Scale distribution (mu = 0, sigma = 1, nu = 5) truncated at [-1, 1]")
 legend ("Truncated PDF", "Histogram")

 ## This demonstrates truncating a t Location-Scale distribution to a specific
 ## range and visualizing the resulting distribution with random samples.

warning: tlsfit: maximum number of iterations are exceeded.
warning: called from
    tlsfit at line 136 column 7
    fit at line 781 column 19
    fitdist at line 683 column 22
    build_DEMOS at line 94 column 11
    classdef_texi2html at line 310 column 16
    package_texi2html at line 288 column 9

tLocationScaleDistribution: v = var (pd)

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

Example: 1


 ## Compute the variance for a t Location-Scale distribution
 data = tlsrnd (0, 1, 5, 10000, 1);
 pd = fitdist (data, "tLocationScale");
 var_value = var (pd)

 ## Use this to calculate the variance, which quantifies the spread of the
 ## distribution, useful for statistical analysis of variability.

var_value = 1.7420

Examples

 pd_fixed = makedist ("tLocationScale", "mu", 0, "sigma", 1, "nu", 5);
 rand ("seed", 2);
 data = random (pd_fixed, 5000, 1);
 pd_fitted = fitdist (data, "tLocationScale");
 plot (pd_fitted);
 msg = "Fitted t Location-Scale distribution with mu = %0.2f, sigma = %0.2f, nu = %0.2f";
 title (sprintf (msg, pd_fitted.mu, pd_fitted.sigma, pd_fitted.nu));

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Class Definition: tLocationScaleDistribution

statistics: tLocationScaleDistribution

Properties

mu

Example: 1

Example: 2

sigma

Example: 1

Example: 2

nu

Example: 1

Example: 2

DistributionName

NumParameters

ParameterNames

ParameterDescription

ParameterValues

ParameterCovariance

ParameterIsFixed

Truncation

IsTruncated

InputData

Methods

cdf

tLocationScaleDistribution: p = cdf (pd, x)

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

Example: 1

icdf

tLocationScaleDistribution: x = icdf (pd, p)

Example: 1

iqr

tLocationScaleDistribution: r = iqr (pd)

Example: 1

mean

tLocationScaleDistribution: m = mean (pd)

Example: 1

median

tLocationScaleDistribution: m = median (pd)

Example: 1

negloglik

Class Definition: `tLocationScaleDistribution`

`mu`

`sigma`

`nu`

`DistributionName`

`NumParameters`

`ParameterNames`

`ParameterDescription`

`ParameterValues`

`ParameterCovariance`

`ParameterIsFixed`

`Truncation`

`IsTruncated`

`InputData`

`cdf`

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

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

`icdf`

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

`iqr`

`tLocationScaleDistribution: r = iqr (pd)`

`mean`

`tLocationScaleDistribution: m = mean (pd)`

`median`

`tLocationScaleDistribution: m = median (pd)`

`negloglik`

`tLocationScaleDistribution: nlogL = negloglik (pd)`

`paramci`

`tLocationScaleDistribution: ci = paramci (pd)`

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

`pdf`

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

`plot`

`tLocationScaleDistribution: plot (pd)`

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

`tLocationScaleDistribution: h = plot (…)`

`proflik`

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

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

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

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

`random`

`tLocationScaleDistribution: r = random (pd)`

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

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

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

`std`

`tLocationScaleDistribution: s = std (pd)`

`truncate`

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

`var`

`tLocationScaleDistribution: v = var (pd)`