Fit a Distribution Using the Distribution Fitter App

This example shows how you can use the Distribution Fitter app to interactively fit a probability distribution to data.

`load carsmall`

Step 2: Import Data

Open the Distribution Fitter tool.

`distributionFitter`

To import the vector `MPG` into the Distribution Fitter app, click the button. The Data dialog box opens.

The Data field displays all numeric arrays in the MATLAB® workspace. From the drop-down list, select `MPG`. A histogram of the selected data appears in the Data preview pane.

In the Data set name field, type a name for the data set, such as `MPG data`, and click . The main window of the Distribution Fitter app now displays a larger version of the histogram in the Data preview pane.

Step 3: Create a New Fit

To fit a distribution to the data, in the main window of the Distribution Fitter app, click .

To fit a normal distribution to `MPG data`:

1. In the Fit name field, enter a name for the fit, such as `My fit`.

2. From the drop-down list in the Data field, select `MPG data`.

3. Confirm that `Normal` is selected from the drop-down menu in the Distribution field.

4. Click .

The Results pane displays the mean and standard deviation of the normal distribution that best fits ```MPG data```.

The Distribution Fitter app main window displays a plot of the normal distribution with this mean and standard deviation.

Based on the plot, a normal distribution does not appear to provide a good fit for the `MPG` data. To obtain a better evaluation, select `Probability plot` from the Display type drop-down list. Confirm that the Distribution drop-down list is set to `Normal`. The main window displays the following figure.

The normal probability plot shows that the data deviates from normal, especially in the tails.

Step 4: Create and Manage Additional Fits

The `MPG` data pdf indicates that the data has two peaks. Try fitting a nonparametric kernel distribution to obtain a better fit for this data.

1. Click Manage Fits. In the dialog box, click .

2. In the Fit name field, enter a name for the fit, such as `Kernel fit`.

3. From the drop-down list in the Data field, select `MPG data`.

4. From the drop-down list in the Distribution field, select Non-parametric. This enables several options in the Non-parametric pane, including Kernel, Bandwidth, and Domain. For now, accept the default value to apply a normal kernel shape and automatically determine the kernel bandwidth (using Auto). For more information about nonparametric kernel distributions, see Kernel Distribution.

5. Click .

The Results pane displays the kernel type, bandwidth, and domain of the nonparametric distribution fit to ```MPG data```.

The main window displays plots of the original ```MPG data``` with the normal distribution and nonparametric kernel distribution overlaid. To visually compare these two fits, select ```Density (PDF)``` from the Display type drop-down list.

To include only the nonparametric kernel fit line (```Kernel fit```) on the plot, click Manage Fits. In the Table of fits pane, locate the row for the normal distribution fit (`My fit`) and clear the box in the Plot column.