How to use df. rolling (..., win type= 'exponential'). mean()

I want to calculate a weighted moving average using df.rolling().mean(). The weights for the values in the window can be set using the win_type parameter. Some parameter values (read more here), also require the input of an additional argument.

# здесь дополнительный аргумент std в методе .mean()
df.rolling(window=21, min_periods=10, win_type='gaussian').mean(std=1) 
# работает

But when it comes to win_type='exponential'

`df.rolling(window=21, min_periods=10, win_type='exponential').mean(tau=10)
# ValueError: The 'exponential' window needs one or more parameters -- pass a tuple.

Can you tell me how to use the exponentially weighted moving average win_type='exponential correctly?

UPD: Added df

Dan Seth a

a = pd.DataFrame([[1, 20, 1], [2, 22, 1], [3, 23, 0], [1, 19, 1], [2, 24, 0],
                 [2, 21, 1], [1, 17, 1], [2, 29, 0], [2, 27, 0]],
                 columns=['type', 'size', 'target'])

All conversions except win_type='exponential' work

a = a.assign(rolling_col=a.groupby(['type'])['size'].transform(
lambda x: x.rolling(2, min_periods=1, win_type='gaussian').mean(std=0.1)))

Will give the output

  type size target rolling_col
    1   20  1   20.0 # В данному примере rolling_col рассчитан при помощи win_type='gaussian'
    2   22  1   22.0 # a должен быть рассчитан при win_type='exponential'
    3   23  0   23.0
    1   19  1   19.5
    2   24  0   23.0
    2   21  1   22.5
    1   17  1   18.0
    2   29  0   25.0
    2   27  0   28.0

Does not work with win_type='exponential', outputs:

 # ValueError: The 'exponential' window needs one or more parameters -- pass a tuple.