# EqualFrequencyDiscretiser#

The `EqualFrequencyDiscretiser()` sorts continuous numerical variables into contiguous equal frequency intervals, that is, intervals that contain approximately the same proportion of observations. The limits of the intervals are calculated according to percentiles or quantiles utilising `pandas.qcut()`. You decide the number of intervals.

A note on number of intervals

Common values are 5 and 10. Note that if the variable is highly skewed or not continuous smaller intervals maybe required. Otherwise, the transformer will introduce np.nan.

The `EqualFrequencyDiscretiser()` works only with numerical variables. A list of variables can be indicated, or the discretiser will automatically select all numerical variables in the train set.

Example

Let’s look at an example using the House Prices Dataset (more details about the dataset here).

Let’s load the house prices dataset and separate it into train and test sets:

```import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split

from feature_engine.discretisation import EqualFrequencyDiscretiser

# Separate into train and test sets
X_train, X_test, y_train, y_test =  train_test_split(
data.drop(['Id', 'SalePrice'], axis=1),
data['SalePrice'], test_size=0.3, random_state=0)
```

Now we want to discretise the 2 variables indicated below into 10 intervals of equal number of observations:

```# set up the discretisation transformer
disc = EqualFrequencyDiscretiser(q=10, variables=['LotArea', 'GrLivArea'])

# fit the transformer
disc.fit(X_train)
```

With `fit()` the transformer learns the boundaries of each interval. Then, we can go ahead and sort the values into the intervals:

```# transform the data
train_t= disc.transform(X_train)
test_t= disc.transform(X_test)
```

The `binner_dict_` stores the interval limits identified for each variable.

```disc.binner_dict_
```
```{'LotArea': [-inf,
5007.1,
7164.6,
8165.700000000001,
8882.0,
9536.0,
10200.0,
11046.300000000001,
12166.400000000001,
14373.9,
inf],
'GrLivArea': [-inf,
912.0,
1069.6000000000001,
1211.3000000000002,
1344.0,
1479.0,
1603.2000000000003,
1716.0,
1893.0000000000005,
2166.3999999999996,
inf]}
```

With equal frequency discretisation, each bin contains approximately the same number of observations.

```train_t.groupby('GrLivArea')['GrLivArea'].count().plot.bar()
plt.ylabel('Number of houses')
```

We can see below that the intervals contain approximately the same number of observations.

Discretisation plus encoding

If we return the interval values as integers, the discretiser has the option to return the transformed variable as integer or as object. Why would we want the transformed variables as object?

Categorical encoders in Feature-engine are designed to work with variables of type object by default. Thus, if you wish to encode the returned bins further, say to try and obtain monotonic relationships between the variable and the target, you can do so seamlessly by setting `return_object` to True. You can find an example of how to use this functionality here.

## More details#

Check also for more details on how to use this transformer: