Distribution Fitter

Fit probability distributions to data

Description

The Distribution Fitter app interactively fits probability distributions to data imported from the MATLAB^® workspace. You can choose from 22 built-in probability distributions or create your own custom distribution. The app displays plots of the fitted distribution superimposed on a histogram of the data. Available plots include probability density function (pdf), cumulative distribution function (cdf), probability plots, and survivor functions. You can export the fitted parameter values to the workspace as a probability distribution object, and use object functions to perform further analyses. For more information on working with these objects, see Working with Probability Distributions. For the programmatic work flow of the Distribution Fitter app, see distributionFitter.

More

Required Products

• MATLAB

• Statistics and Machine Learning Toolbox™

×

Open the Distribution Fitter App

• MATLAB Toolstrip: On the Apps tab, under Math, Statistics and Optimization, click the app icon.

• MATLAB command prompt: Enter distributionFitter.

Examples

• Fit a Distribution Using the Distribution Fitter App

Parameters

Data

Data — Data to import from the workspace

list of variables | valid MATLAB expression

Specify the data to import by selecting a variable from the drop-down list. If the variable is a matrix, the app imports the first column of the matrix by default. To select a different column or row of the matrix, click Select Column or Row. Alternatively, you can enter any valid MATLAB expression in the field.

Censoring — Variable containing censoring data

list of variables

Specify the censoring data by selecting a variable from the drop-down list. If the variable is a matrix, the app imports the first column of the matrix by default. To select a different column or row of the matrix, click Select Column or Row. This parameter is optional.

Frequency — Variable containing frequency data

list of variables

Specify the frequency data by selecting a variable from the drop-down list. If the variable is a matrix, the app imports the first column of the matrix by default. To select a different column or row of the matrix, click Select Column or Row. This parameter is optional.

Data set name — Data set name

text

Enter a name for the data set or accept the default name.

Manage data sets — Manage previously imported data sets

list of data sets

Manage previously imported data sets. Click the data set of interest, then click the buttons below this pane to view the data (View), set the bin rules (Set Bin Rules), rename the data set (Rename), or delete the data set (Delete).

Data preview — Preview plot of data

histogram plot

Display a preview plot of the variable selected from the Data drop-down menu.

New fit

Fit name — Name of fit

text

Enter a name for the fit or accept the default name.

Data — Data set to fit

list of data sets

Specify the data to fit by selecting a data set from the drop-down list.

Distribution — Distribution to fit

Normal (default) | Exponential | Weibull | Non-parametric | ...

Specify the distribution to fit by selecting a distribution name from the drop-down list.

Exclusion rule — Data exclusion rule

list of exclusion rules

Specify a rule to exclude some data values by selecting an exclusion rule from the drop-down list. To populate this drop-down list, you must first define exclusion rules by clicking Exclude in the main window of the app. This parameter is optional

Manage fits

Plot — Flag to plot fitted distribution

checked (default) | unchecked

Specify which fit or fits to plot in the main window by selecting the Plot check box next to each fit. Clear the Plot check box to remove a fit from the plot.

Conf bounds — Flag to plot confidence bounds

unchecked (default) | checked

If you select Plot for a particular fit, you can select Conf bounds to display the confidence bounds for that fit on the plot in the main window. Clearing the Conf bounds check box removes the confidence intervals from the plot. The Distribution Fitter app displays confidence bounds only if the Display Type in the main window is set to Cumulative probability (CDF), Quantile (inverse CDF), Survivor function, or Cumulative hazard.

Evaluate

Fit — Fit to evaluate

list of fits

Select one or more fits from the list to evaluate.

Function — Available functions to fit

Density (PDF) (default) | Cumulative probability (CDF) | Quantile (inverse CDF) | Survivor function | Cumulative hazard | Hazard rate

Specify the type of probability function to evaluate from the drop-down list. Available probability functions include the probability density function (pdf), cumulative distribution function (cdf), quantile (inverse cdf), survival function, cumulative hazard, and hazard rate.

At x = — Values at which to evaluate function

numeric vector

Specify a numeric vector of values at which to evaluate the function. If you specify Function as Quantile (inverse CDF), this field name changes to At p = and you enter a vector of probability values.

Compute confidence bounds — Flag to compute confidence bounds

unchecked (default) | checked

Select Compute confidence bounds to compute the confidence bounds for the selected fit. This check box is enabled only if you specify Function as Cumulative probability (CDF), Quantile (inverse CDF), Survivor function, or Cumulative hazard. This parameter is optional.

Level — Level for confidence bounds

95% (default) | numeric value

Specify the level at which to compute the confidence bounds. This check box is enabled only if you specify Function as Cumulative probability (CDF), Quantile (inverse CDF), Survivor function, or Cumulative hazard.

Plot function — Flag to plot function

unchecked (default) | checked

Select Plot function to display a plot of the distribution function, evaluated at the points that you enter in the At x = field, in a new window. This parameter is optional.

Exclude

Exclusion rule name — Name of exclusion rule

text

Enter a name for the exclusion rule.

Exclude sections — Define data exclusion rules numerically

numeric value

Specify lower and upper limits for the data numerically.

Exclude graphically — Define data exclusion rules graphically

list of variables

Specify lower and upper limits for the data by selecting a variable from the Select data drop-down list and clicking Exclude Graphically. An interactive plot opens in a new window, where you can add lower or upper limits by clicking and dragging a boundary on the plot.

Existing exclusion rules — List of existing exclusion rules

list of exclusion rules

Select an existing exclusion rule from the list. You can copy, view, rename, or delete exclusion rules by clicking the appropriate button.

Programmatic Use

distributionFitter

distributionFitter opens the Distribution Fitter app, or brings focus to the app if it is already open.

distributionFitter(y)

distributionFitter(y) opens the Distribution Fitter app populated with the data specified by the vector y.

distributionFitter(y,cens)

distributionFitter(y,cens) uses the vector cens to specify whether the observation y(j) is censored, (cens(j)==1), or observed exactly, (cens(j)==0). If cens is omitted or empty, then no y values are censored.

distributionFitter(y,cens,freq)

distributionFitter(y,cens,freq) uses the vector freq to specify the frequency of each element contained in y. If freq is omitted or empty, then all values in y have a frequency of 1.

distributionFitter(y,cens,freq,dsname)

distributionFitter(y,cens,freq,dsname) creates a data set with the name dsname using the data vector, y, censoring indicator, cens, and frequency vector, freq. Specify dsname as a character vector or string scalar, for example, 'mydata'.

Version History

Introduced before R2006a

R2024a: Distribution Fitter app uses the MATLAB default color scheme

Starting in R2024a, the Distribution Fitter app uses the MATLAB default color scheme instead of static colors to determine the colors of graphics objects.