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Working with Distributions Through GUIs

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Exploring Distributions

Modeling Your Data Using the Distribution Fitting GUI

Visually Exploring Random Number Generation

This section describes Statistics Toolbox GUIs that provide convenient, interactive access to the distribution functions described in Statistics Toolbox Distribution Functions.

Exploring Distributions

To interactively see the influence of parameter changes on the shapes of the pdfs and cdfs of supported Statistics Toolbox distributions, use the Probability Distribution Function Tool.

Run the tool by typing disttool at the command line.

Start by selecting a distribution. Then choose the function type: probability density function (pdf) or cumulative distribution function (cdf).

Once the plot displays, you can

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Modeling Your Data Using the Distribution Fitting GUI

The Distribution Fitting Tool is a GUI for fitting univariate distributions to data. This section describes how to use the Distribution Fitting Tool and covers the following topics:

Starting the Distribution Fitting Tool (Subsections to be rearranged)

To open the Distribution Fitting Tool, enter the command

dfittool

The following figure shows the main window of the Distribution Fitting Tool.

Adjusting the Plot.   Buttons at the top of the tool allow you to adjust the plot displayed in the main window:

Displaying the Data.   The Display Type field specifies the type of plot displayed in the main window. Each type corresponds to a probability function, for example, a probability density function. The following display types are available:

Inputting and Fitting Data.   The task buttons enable you to perform the tasks necessary to fit distributions to data. Each button opens a new window in which you perform the task. The buttons include

(This section will be integrated elsewhere).   The display pane displays plots of the data sets and fits you create. Whenever you make changes in one of the task windows, the results are updated in the display pane.

Saving and Customizing Distributions.   The Distribution Fitting Tool menus contain items that enable you to do the following:

Example: Fitting a Distribution (to be rearranged)

This section presents an example that illustrates how to use the Distribution Fitting Tool. The example involves the following steps:

Step 1: Generate Random Data.   To try the example, first generate some random data to which you will fit a distribution. The following command generates a vector data, of length 100, whose entries are random numbers from a normal distribution with mean.36 and standard deviation 1.4.

data = normrnd(.36, 1.4, 100, 1);

Step 2: Import Data.   To import the vector data into the Distribution Fitting Tool, click the Data button in main window. This opens the window shown in the following figure.

The Data field displays all numeric arrays in the MATLAB workspace. Select data from the drop-down list, as shown in the following figure.

This displays a histogram of the data in the Data preview pane.

In the Data set name field, type a name for the data set, such as My data, and click Create Data Set to create the data set. The main window of the Distribution Fitting Tool now displays a larger version of the histogram in the Data preview pane, as shown in the following figure.

Step 3: Create a New Fit.   To fit a distribution to the data, click New Fit in the main window of the Distribution Fitting Tool. This opens the window shown in the following figure.

To fit a normal distribution, the default entry of the Distribution field, to My data:

  1. Enter a name for the fit, such as My fit, in the Fit name field.

  2. Select My data from the drop-down list in the Data field.

  3. Click Apply.

The Results pane displays the mean and standard deviation of the normal distribution that best fits My data, as shown in the following figure.

The main window of the Distribution Fitting Tool displays a plot of the normal distribution with this mean and standard deviation, as shown in the following figure.

Creating and Managing Data Sets

This section describes how create and manage data sets.

To begin, click the Data button in the main window of the Distribution Fitting Tool to open the Data window shown in the following figure.

Importing Data.   The Import workspace vectors pane enables you to create a data set by importing a vector from the MATLAB workspace. The following sections describe the fields of the Import workspace vectors pane and give appropriate values for vectors imported from the MATLAB workspace:

After you have entered the information in the preceding fields, click Create Data Set to create the data set My data.

Managing Data Sets.   The Manage data sets pane enables you to view and manage the data sets you create. When you create a data set, its name appears in the Data sets list. The following figure shows the Manage data sets pane after creating the data set My data.

For each data set in the Data sets list, you can

The Distribution Fitting Tool cannot display confidence bounds on density (PDF), quantile (inverse CDF), or probability plots. Clearing the Bounds check box removes the confidence bounds from the plot in the main window.

When you select a data set from the list, the following buttons are enabled:

Setting Bin Rules.   To set bin rules for the histogram of a data set, click Set Bin Rules. This opens the dialog box shown in the following figure.

You can select from the following rules:

The Set Bin Width Rules dialog box also provides the following options:

Creating a New Fit

This section describes how to create a new fit. To begin, click the New Fit button at the top of the main window to open a New Fit window. If you created the data set My data, it appears in the Data field:

Field NameDescription
Fit NameEnter a name for the fit in the Fit Name field.
Data

The Data field contains a drop-down list of the data sets you have created. Select the data set to which you want to fit a distribution.

Distribution

Select the type of distribution you want to fit from the Distribution drop-down list. See Available Distributions for a list of distributions supported by the Distribution Fitting Tool.

Only the distributions that apply to the values of the selected data set are displayed in the Distribution field. For example, positive distributions are not displayed when the data include values that are zero or negative.

You can specify either a parametric or a nonparametric distribution. When you select a parametric distribution from the drop-down list, a description of its parameters is displayed in the pane below the Exclusion rule field. The Distribution Fitting Tool estimates these parameters to fit the distribution to the data set. When you select Nonparametric fit, options for the fit appear in the pane, as described in Further Options for Nonparametric Fits.

Exclusion RuleYou can specify a rule to exclude some the data in the Exclusion rule field. You can create an exclusion rule by clicking Exclude in the main window of the Distribution Fitting Tool. For more information, see Excluding Data.

Apply the New Fit.   Click Apply to fit the distribution. For a parametric fit, the Results pane displays the values of the estimated parameters. For a nonparametric fit, the Results pane displays information about the fit.

When you click Apply, the main window of Distribution Fitting Tool displays a plot of the distribution, along with the corresponding data.

Available Distributions.   This section lists the distributions available in the Distribution Fitting Tool.

Most, but not all, of the distributions available in the Distribution Fitting Tool are supported elsewhere in Statistics Toolbox software (see Supported Distributions), and have dedicated distribution fitting functions. These functions are used to compute the majority of the fits in the Distribution Fitting Tool, and are referenced in the list below.

Other fits are computed using functions internal to the Distribution Fitting Tool. Distributions that do not have corresponding Statistics Toolbox fitting functions are described in Additional Distributions Available in the Distribution Fitting Tool.

Not all of the distributions listed below are available for all data sets. The Distribution Fitting Tool determines the extent of the data (nonnegative, unit interval, etc.) and displays appropriate distributions in the Distribution drop-down list. Distribution data ranges are given parenthetically in the list below.

Further Options for Nonparametric Fits.   When you select Non-parametric in the Distribution field, a set of options appears in the pane below Exclusion rule, as shown in the following figure.

The options for nonparametric distributions are

Displaying Results

This section explains the different ways to display results in the main window of the Distribution Fitting Tool. The main window displays plots of

The following fields are available.

Display Type.   The Display Type field in the main window specifies the type of plot displayed. Each type corresponds to a probability function, for example, a probability density function. The following display types are available:

Confidence Bounds.   You can display confidence bounds for data sets and fits, provided that you set Display Type to Cumulative probability (CDF), Survivor function, Cumulative hazard, or Quantile for fits only.

To set the confidence level for the bounds, select Confidence Level from the View menu in the main window and choose from the options.

Managing Fits

This section describes how to manage fits that you have created. To begin, click the Manage Fits button in the main window of the Distribution Fitting Tool. This opens the Fit Manager window as shown in the following figure.

The Table of fits displays a list of the fits you create, with the following options:

Evaluating Fits

The Evaluate window enables you to evaluate any fit at whatever points you choose. To open the window, click the Evaluate button in the main window of the Distribution Fitting Tool. The following figure shows the Evaluate window.

The Evaluate window contains the following items:

Click Apply to apply these settings to the selected fit. The following figure shows the results of evaluating the cumulative density function for the fit My fit, created in Example: Fitting a Distribution (to be rearranged), at the points in the vector -3:0.5:3.

The window displays the following values in the columns of the table to the right of the Fit pane:

To save the data displayed in the Evaluate window, click Export to Workspace. This saves the values in the table to a matrix in the MATLAB workspace.

Excluding Data

To exclude values from fit, click the Exclude button in the main window of the Distribution Fitting Tool. This opens the Exclude window, in which you can create rules for excluding specified values. You can use these rules to exclude data when you create a new fit in the New Fit window. The following figure shows the Exclude window.

To create an exclusion rule:

  1. Exclusion Rule Name—Enter a name for the exclusion rule in the Exclusion rule name field.

  2. Exclude Sections—In the Exclude sections pane, you can specify bounds for the excluded data:

    • In the Lower limit: exclude Y drop-down list, select <= or < from the drop-down list and enter a scalar in the field to the right. This excludes values that are either less than or equal to or less than that scalar, respectively.

    • In the Upper limit: exclude Y drop-down list, select >= or > from the drop-down list and enter a scalar in the field to the right to exclude values that are either greater than or equal to or greater than the scalar, respectively.

    OR

    Exclude Graphically—The Exclude Graphically button enables you to define the exclusion rule by displaying a plot of the values in a data set and selecting the bounds for the excluded data with the mouse. For example, if you created the data set My data, described in Creating and Managing Data Sets, select it from the drop-down list next to Exclude graphically and then click the Exclude graphically button. This displays the values in My data in a new window as shown in the following figure.

    To set a lower limit for the boundary of the excluded region, click Add Lower Limit. This displays a vertical line on the left side of the plot window. Move the line with the mouse to the point you where you want the lower limit, as shown in the following figure.

    Moving the vertical line changes the value displayed in the Lower limit: exclude data field in the Exclude window, as shown in the following figure.

    The value displayed corresponds to the x-coordinate of the vertical line.

    Similarly, you can set the upper limit for the boundary of the excluded region by clicking Add Upper Limit and moving the vertical line that appears at the right side of the plot window. After setting the lower and upper limits, click Close and return to the Exclude window.

  3. Create Exclusion Rule—Once you have set the lower and upper limits for the boundary of the excluded data, click Create Exclusion Rule to create the new rule. The name of the new rule now appears in the Existing exclusion rules pane.

    When you select an exclusion rule in the Existing exclusion rules pane, the following buttons are enabled:

    • Copy — Creates a copy of the rule, which you can then modify. To save the modified rule under a different name, click Create Exclusion Rule.

    • View — Opens a new window in which you can see which data points are excluded by the rule. The following figure shows a typical example.

      The shaded areas in the plot graphically display which data points are excluded. The table to the right lists all data points. The shaded rows indicate excluded points:

    • Rename — Renames the rule

    • Delete — Deletes the rule

    Once you define an exclusion rule, you can use it when you fit a distribution to your data. The rule does not exclude points from the display of the data set.

Saving and Loading Sessions

This section explains how to save your work in the current Distribution Fitting Tool session and then load it in a subsequent session, so that you can continue working where you left off.

Saving a Session.   To save the current session, select Save Session from the File menu in the main window. This opens a dialog box that prompts you to enter a filename, such as my_session.dfit, for the session. Clicking Save saves the following items created in the current session:

Loading a Session.   To load a previously saved session, select Load Session from the File menu in the main window and enter the name of a previously saved session. Clicking Open restores the information from the saved session to the current session of the Distribution Fitting Tool.

Generating an M-File to Fit and Plot Distributions

The Generate M-file option in the File menu enables you to create an M-file that

After you end the current session, you can use the M-file to create plots in a standard MATLAB figure window, without having to reopen the Distribution Fitting Tool.

As an example, assuming you created the fit described in Creating a New Fit, do the following steps:

  1. Select Generate M-file from the File menu.

  2. Save the M-file as normal_fit.m in a folder on the MATLAB path.

You can then apply the function normal_fit to any vector of data in the MATLAB workspace. For example, the following commands

new_data = normrnd(4.1, 12.5, 100, 1);
normal_fit(new_data)
legend('New Data', 'My fit')

fit a normal distribution to a data set and generate a plot of the data and the fit.

Using Custom Distributions

This section explains how to use custom distributions with the Distribution Fitting Tool.

Defining Custom Distributions.   To define a custom distribution, select Define Custom Distribution from the File menu. This opens an M-file template in the MATLAB editor. You then edit this M-file so that it computes the distribution you want.

The template includes example code that computes the Laplace distribution, beginning at the lines

% -----------------------------
% -- Remove the following return statement to define the 
% -- Laplace distributon
% -----------------------------
return

To use this example, simply delete the command return and save the M-file. If you save the template in a folder on the MATLAB path, under its default name dfittooldists.m, the Distribution Fitting Tool reads it in automatically when you start the tool. You can also save the template under a different name, such as laplace.m, and then import the custom distribution as described in the following section.

Importing Custom Distributions.   To import a custom distribution, select Import Custom Distributions from the File menu. This opens a dialog box in which you can select the M-file that defines the distribution. For example, if you created the file laplace.m, as described in the preceding section, you can enter laplace.m and select Open in the dialog box. The Distribution field of the New Fit window now contains the option Laplace.

Additional Distributions Available in the Distribution Fitting Tool

The following distributions are available in the Distribution Fitting Tool, but do not have dedicated distribution functions as described in Statistics Toolbox Distribution Functions. The distributions can be used with the functions pdf, cdf, icdf, and mle in a limited capacity. See the reference pages for these functions for details on the limitations.

For a complete list of the distributions available for use with the Distribution Fitting Tool, see Supported Distributions. Distributions listing dfittool in the fit column of the tables in that section can be used with the Distribution Fitting Tool.

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Visually Exploring Random Number Generation

The Random Number Generation Tool is a graphical user interface that generates random samples from specified probability distributions and displays the samples as histograms. Use the tool to explore the effects of changing parameters and sample size on the distributions.

Run the tool by typing randtool at the command line.

Start by selecting a distribution, then enter the desired sample size.

You can also

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Supported DistributionsSupported Distributions Statistics Toolbox Distribution FunctionsStatistics Toolbox Distribution Functions

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