> ## Documentation Index
> Fetch the complete documentation index at: https://nixtlaverse.nixtla.io/llms.txt
> Use this file to discover all available pages before exploring further.

# Exponentially weighted

> Compute exponentially weighted mean

##

### `exponentially_weighted_mean`

```python theme={null}
exponentially_weighted_mean(x, alpha, skipna=False)
```

Compute the exponentially weighted mean of the input array.

**Parameters:**

| Name     | Type                                   | Description                                                                                                                                                                                                                                                                               | Default            |
| -------- | -------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------ |
| `x`      | <code>[ndarray](#numpy.ndarray)</code> | Input array.                                                                                                                                                                                                                                                                              | *required*         |
| `alpha`  | <code>[float](#float)</code>           | Weight parameter.                                                                                                                                                                                                                                                                         | *required*         |
| `skipna` | <code>[bool](#bool)</code>             | If True, exclude NaN values from calculations using forward-fill behavior. When False (default), any NaN value causes the result to be NaN, maintaining backwards compatibility. When True, the last valid value is forward-filled through NaN values (matching pandas default behavior). | <code>False</code> |

**Returns:**

| Type                                   | Description                                             |
| -------------------------------------- | ------------------------------------------------------- |
| <code>[ndarray](#numpy.ndarray)</code> | np.ndarray: Array with the exponentially weighted mean. |

**Examples:**

```pycon theme={null}
>>> import numpy as np
>>> x = np.array([1.0, 2.0, np.nan, 4.0, 5.0])
>>> # Default behavior: NaN propagates
>>> exponentially_weighted_mean(x, alpha=0.5)
array([1., 1.5, nan, nan, nan])
>>> # With skipna=True: forward-fill through NaN
>>> exponentially_weighted_mean(x, alpha=0.5, skipna=True)
array([1., 1.5, 1.5, 2.75, 3.875])
```