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# How to Perform a Box-Cox Transformation in Python

AÂ box-cox transformation is a commonly used method for transforming a non-normally distributed dataset into a more normally distributed one.

The basic idea behind this method is to find some value for Î» such that the transformed data is as close to normally distributed as possible, using the following formula:

• y(Î») = (yÎ» â€“ 1) / Î»Â  if y â‰  0
• y(Î») = log(y)Â  if y = 0

We can perform a box-cox transformation in Python by using the scipy.stats.boxcox() function.

The following example shows how to use this function in practice.

### Example: Box-Cox Transformation in Python

Suppose we generate a random set of 1,000 values that come from an exponential distribution:

```#load necessary packages
import numpy as np
from scipy.stats import boxcox
import seaborn as sns

#make this example reproducible
np.random.seed(0)

#generate dataset
data = np.random.exponential(size=1000)

#plot the distribution of data values
sns.distplot(data, hist=False, kde=True)
```

We can see that the distribution does not appear to be normal.

We can use theÂ boxcox() function to find an optimal value of lambda that produces a more normal distribution:

```#perform Box-Cox transformation on original data
transformed_data, best_lambda = boxcox(data)

#plot the distribution of the transformed data values
sns.distplot(transformed_data, hist=False, kde=True) ```

We can see that the transformed data follows much more of a normal distribution.

We can also find the exact lambda value used to perform the Box-Cox transformation:

```#display optimal lambda value
print(best_lambda)

0.2420131978174143
```

The optimal lambda was found to be roughly 0.242.

Thus, each data value was transformed using the following equation:

New = (old0.242 â€“ 1) / 0.242

We can confirm this by looking at the values from the original data compared to the transformed data:

```#view first five values of original dataset
data[0:5]

array([0.79587451, 1.25593076, 0.92322315, 0.78720115, 0.55104849])

#view first five values of transformed dataset
transformed_data[0:5]

array([-0.22212062,  0.23427768, -0.07911706, -0.23247555, -0.55495228])
```

The first value in the original dataset was 0.79587. Thus, we applied the following formula to transform this value:

New = (.795870.242 â€“ 1) / 0.242 =Â -0.222

We can confirm that the first value in the transformed dataset is indeedÂ -0.222.