## Gaussian Models

### About Gaussian Models

The Gaussian model fits peaks, and is given by

$$y={\displaystyle \sum _{i=1}^{n}{a}_{i}{e}^{\left[-{\left(\frac{x-{b}_{i}}{{c}_{i}}\right)}^{2}\right]}}$$

where *a* is the amplitude, *b* is
the centroid (location), *c* is related to the peak
width, *n* is the number of peaks to fit, and 1 ≤ *n* ≤
8.

Gaussian peaks are encountered in many areas of science and
engineering. For example, Gaussian peaks can describe line emission
spectra and chemical concentration assays.

### Fit Gaussian Models Interactively

Open the Curve Fitting app by entering `cftool`

.
Alternatively, click Curve Fitting on the Apps tab.

In the Curve Fitting app, select curve data (**X
data** and **Y data**, or just **Y
data** against index).

Curve Fitting app creates the default curve fit, `Polynomial`

.

Change the model type from `Polynomial`

to `Gaussian`

.

You can specify the following options:

Choose the number of terms: `1`

to `8`

.

Look in the **Results** pane to see the model
terms, the values of the coefficients, and the goodness-of-fit statistics.

(Optional) Click **Fit Options** to
specify coefficient starting values and constraint bounds, or change
algorithm settings.

The toolbox calculates optimized start points for Gaussian models,
based on the current data set. You can override the start points and
specify your own values in the Fit Options dialog box.

Gaussians have the width parameter `c1`

constrained
with a lower bound of `0`

. The default lower bounds
for most library models are `-Inf`

, which indicates
that the coefficients are unconstrained.

For more information on the settings, see Specifying Fit Options and Optimized Starting Points.

### Fit Gaussian Models Using the fit Function

This example shows how to use the `fit`

function to fit a Gaussian model to data.

The Gaussian library model is an input argument to the `fit`

and `fittype`

functions. Specify the model type `gauss`

followed by the number of terms, e.g., `'gauss1'`

through `'gauss8'`

.

**Fit a Two-Term Gaussian Model**

Load some data and fit a two-term Gaussian model.

f =
General model Gauss2:
f(x) = a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2)
Coefficients (with 95% confidence bounds):
a1 = 1.47 (1.426, 1.515)
b1 = 897.7 (897, 898.3)
c1 = 27.08 (26.08, 28.08)
a2 = 0.6994 (0.6821, 0.7167)
b2 = 810.8 (790, 831.7)
c2 = 592.9 (500.1, 685.7)

## See Also

`fit`

| `fitoptions`

| `fittype`

## Related Examples