pastas.stats.metrics.pearsonr
=============================

.. py:function:: pastas.stats.metrics.pearsonr(obs: pandas.Series, sim: pandas.Series, missing: str = 'drop', weighted: bool = False, max_gap: int = 30) -> float

   
   Compute the (weighted) Pearson correlation (r).

   :param obs: The Series with the observed values.
   :type obs: pandas.Series
   :param sim: The Series with the simulated values.
   :type sim: pandas.Series
   :param missing: string with the rule to deal with missing values in the observed series. Only
                   "drop" is supported now.
   :type missing: str, optional
   :param weighted: Weight the values by the normalized time step to account for irregular time
                    series. Default is False.
   :type weighted: bool, optional
   :param max_gap: maximum allowed gap period in days to use for the computation of the weights.
                   All time steps larger than max_gap are replace with the max_gap value.
                   Default value is 30 days.
   :type max_gap: int, optional

   .. rubric:: Notes

   The Pearson correlation (r) is computed as follows:

   .. math:: r = \frac{\sum_{i=1}^{N}w_i (y_{o,i} - \bar{y_o})(y_{s,i} - \bar{
       y_s})} {\sqrt{\sum_{i=1}^{N} w_i(y_{o,i}-\bar{y_o})^2 \sum_{i=1}^{N}w_i(
       y_{s,i} -\bar{y_s})^2}}

   Where :math:`y_o` is observed time series, :math:`y_s` the simulated time series,
   and :math:`N` the number of observations in the observed time series.















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