# scipy – How can I fit a gaussian curve in python?

## scipy – How can I fit a gaussian curve in python?

You can use `fit`

from `scipy.stats.norm`

as follows:

```
import numpy as np
from scipy.stats import norm
import matplotlib.pyplot as plt
data = np.random.normal(loc=5.0, scale=2.0, size=1000)
mean,std=norm.fit(data)
```

`norm.fit`

tries to fit the parameters of a normal distribution based on the data. And indeed in the example above `mean`

is approximately 5 and `std`

is approximately 2.

In order to plot it, you can do:

```
plt.hist(data, bins=30, density=True)
xmin, xmax = plt.xlim()
x = np.linspace(xmin, xmax, 100)
y = norm.pdf(x, mean, std)
plt.plot(x, y)
plt.show()
```

The blue boxes are the histogram of your data, and the green line is the Gaussian with the fitted parameters.

There are many ways to fit a gaussian function to a data set. I often use astropy when fitting data, thats why I wanted to add this as additional answer.

I use some data set that should simulate a gaussian with some noise:

```
import numpy as np
from astropy import modeling
m = modeling.models.Gaussian1D(amplitude=10, mean=30, stddev=5)
x = np.linspace(0, 100, 2000)
data = m(x)
data = data + np.sqrt(data) * np.random.random(x.size) - 0.5
data -= data.min()
plt.plot(x, data)
```

Then fitting it is actually quite simple, you specify a model that you want to fit to the data and a fitter:

```
fitter = modeling.fitting.LevMarLSQFitter()
model = modeling.models.Gaussian1D() # depending on the data you need to give some initial values
fitted_model = fitter(model, x, data)
```

And plotted:

```
plt.plot(x, data)
plt.plot(x, fitted_model(x))
```

However you can also use just Scipy but you have to define the function yourself:

```
from scipy import optimize
def gaussian(x, amplitude, mean, stddev):
return amplitude * np.exp(-((x - mean) / 4 / stddev)**2)
popt, _ = optimize.curve_fit(gaussian, x, data)
```

This returns the optimal arguments for the fit and you can plot it like this:

```
plt.plot(x, data)
plt.plot(x, gaussian(x, *popt))
```