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docs(python): Fix formula in ewm_mean_by #18506

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Sep 2, 2024
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docs(python): Fix formula in ewm_mean_by #18506

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23 changes: 12 additions & 11 deletions py-polars/polars/expr/expr.py
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Original file line number Diff line number Diff line change
Expand Up @@ -9311,7 +9311,7 @@ def ewm_mean(
ignore_nulls: bool = False,
) -> Expr:
r"""
Exponentially-weighted moving average.
Compute exponentially-weighted moving average.

Parameters
----------
Expand All @@ -9326,11 +9326,11 @@ def ewm_mean(
.. math::
\alpha = \frac{2}{\theta + 1} \; \forall \; \theta \geq 1
half_life
Specify decay in terms of half-life, :math:`\lambda`, with
Specify decay in terms of half-life, :math:`\tau`, with

.. math::
\alpha = 1 - \exp \left\{ \frac{ -\ln(2) }{ \lambda } \right\} \;
\forall \; \lambda > 0
\alpha = 1 - \exp \left\{ \frac{ -\ln(2) }{ \tau } \right\} \;
\forall \; \tau > 0
alpha
Specify smoothing factor alpha directly, :math:`0 < \alpha \leq 1`.
adjust
Expand Down Expand Up @@ -9393,20 +9393,21 @@ def ewm_mean_by(
half_life: str | timedelta,
) -> Expr:
r"""
Calculate time-based exponentially weighted moving average.
Compute time-based exponentially weighted moving average.

Given observations :math:`x_1, x_2, \ldots, x_n` at times
:math:`t_1, t_2, \ldots, t_n`, the EWMA is calculated as
Given observations :math:`x_0, x_1, \ldots, x_{n-1}` at times
:math:`t_0, t_1, \ldots, t_{n-1}`, the EWMA is calculated as

.. math::

y_0 &= x_0

\alpha_i &= \exp(-\lambda(t_i - t_{i-1}))
\alpha_i &= 1 - \exp \left\{ \frac{ -\ln(2)(t_i-t_{i-1}) }
{ \tau } \right\}

y_i &= \alpha_i x_i + (1 - \alpha_i) y_{i-1}; \quad i > 0

where :math:`\lambda` equals :math:`\ln(2) / \text{half_life}`.
where :math:`\tau` is the `half_life`.

Parameters
----------
Expand Down Expand Up @@ -9490,7 +9491,7 @@ def ewm_std(
ignore_nulls: bool = False,
) -> Expr:
r"""
Exponentially-weighted moving standard deviation.
Compute exponentially-weighted moving standard deviation.

Parameters
----------
Expand Down Expand Up @@ -9581,7 +9582,7 @@ def ewm_var(
ignore_nulls: bool = False,
) -> Expr:
r"""
Exponentially-weighted moving variance.
Compute exponentially-weighted moving variance.

Parameters
----------
Expand Down
23 changes: 12 additions & 11 deletions py-polars/polars/series/series.py
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Original file line number Diff line number Diff line change
Expand Up @@ -6883,7 +6883,7 @@ def ewm_mean(
ignore_nulls: bool = False,
) -> Series:
r"""
Exponentially-weighted moving average.
Compute exponentially-weighted moving average.

Parameters
----------
Expand All @@ -6898,11 +6898,11 @@ def ewm_mean(
.. math::
\alpha = \frac{2}{\theta + 1} \; \forall \; \theta \geq 1
half_life
Specify decay in terms of half-life, :math:`\lambda`, with
Specify decay in terms of half-life, :math:`\tau`, with

.. math::
\alpha = 1 - \exp \left\{ \frac{ -\ln(2) }{ \lambda } \right\} \;
\forall \; \lambda > 0
\alpha = 1 - \exp \left\{ \frac{ -\ln(2) }{ \tau } \right\} \;
\forall \; \tau > 0
alpha
Specify smoothing factor alpha directly, :math:`0 < \alpha \leq 1`.
adjust
Expand Down Expand Up @@ -6958,20 +6958,21 @@ def ewm_mean_by(
half_life: str | timedelta,
) -> Series:
r"""
Calculate time-based exponentially weighted moving average.
Compute time-based exponentially weighted moving average.

Given observations :math:`x_1, x_2, \ldots, x_n` at times
:math:`t_1, t_2, \ldots, t_n`, the EWMA is calculated as
Given observations :math:`x_0, x_1, \ldots, x_{n-1}` at times
:math:`t_0, t_1, \ldots, t_{n-1}`, the EWMA is calculated as

.. math::

y_0 &= x_0

\alpha_i &= \exp(-\lambda(t_i - t_{i-1}))
\alpha_i &= 1 - \exp \left\{ \frac{ -\ln(2)(t_i-t_{i-1}) }
{ \tau } \right\}

y_i &= \alpha_i x_i + (1 - \alpha_i) y_{i-1}; \quad i > 0

where :math:`\lambda` equals :math:`\ln(2) / \text{half_life}`.
where :math:`\tau` is the `half_life`.

Parameters
----------
Expand Down Expand Up @@ -7047,7 +7048,7 @@ def ewm_std(
ignore_nulls: bool = False,
) -> Series:
r"""
Exponentially-weighted moving standard deviation.
Compute exponentially-weighted moving standard deviation.

Parameters
----------
Expand Down Expand Up @@ -7131,7 +7132,7 @@ def ewm_var(
ignore_nulls: bool = False,
) -> Series:
r"""
Exponentially-weighted moving variance.
Compute exponentially-weighted moving variance.

Parameters
----------
Expand Down