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Fit probability distributions to data

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`

.

MATLAB

Statistics and Machine Learning Toolbox™

**Note:** Distribution Fitter does not provide
printing, custom distribution defining, or code generating functionality in
MATLAB
Online™.

MATLAB Toolstrip: On the

**Apps**tab, under**Math, Statistics and Optimization**, click the app icon.MATLAB command prompt: Enter

`distributionFitter`

.

`Data`

— Data to import from the workspacelist 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 datalist 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 datalist 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 namecharacter vector

Specify a name for the data set as a character vector, or accept the default name.

`Manage data sets`

— Manage previously imported data setslist 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 datahistogram plot

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

`Fit name`

— Name of fitcharacter vector

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

`Data`

— Data set to fitlist 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 rulelist 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

`Plot`

— Flag to plot fitted distributionchecked (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 counds`

— Flag to plot confidence boundsunchecked (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**.

`Fit`

— Fit to evaluatelist 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 functionnumeric 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 boundsunchecked (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 bounds95% (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 functionunchecked (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.

`Exclusion rule name`

— Name of exclusion rulecharacter vector

Specify a name for the exclusion rule as a character vector.

`Exclude sections`

— Define data exclusion rules numericallynumeric value

Specify lower and upper limits for the data numerically.

`Exclude graphically`

— Define data exclusion rules graphicallylist 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 ruleslist 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.

`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(`

uses the vector `y`

,`cens`

)`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(`

uses the vector `y`

,`cens`

,`freq`

)`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(`

creates a data set with the name `y`

,`cens`

,`freq`

,`dsname`

)`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'`

.

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