def nrmse_mean(simulated_array, observed_array, replace_nan=None, replace_inf=None,
               remove_neg=False, remove_zero=False):
    """Compute the mean normalized root mean square error between the simulated and observed data.

    .. image:: /pictures/NRMSE_Mean.png

    **Range:** 0 ≤ NRMSE < inf.

    **Notes:** This metric is the RMSE normalized by the mean of the observed time series (x).
    Normalizing allows comparison between data sets with different scales.

    Parameters
    ----------
    simulated_array: one dimensional ndarray
        An array of simulated data from the time series.

    observed_array: one dimensional ndarray
        An array of observed data from the time series.

    replace_nan: float, optional
        If given, indicates which value to replace NaN values with in the two arrays. If None, when
        a NaN value is found at the i-th position in the observed OR simulated array, the i-th value
        of the observed and simulated array are removed before the computation.

    replace_inf: float, optional
        If given, indicates which value to replace Inf values with in the two arrays. If None, when
        an inf value is found at the i-th position in the observed OR simulated array, the i-th
        value of the observed and simulated array are removed before the computation.

    remove_neg: boolean, optional
        If True, when a negative value is found at the i-th position in the observed OR simulated
        array, the i-th value of the observed AND simulated array are removed before the
        computation.

    remove_zero: boolean, optional
        If true, when a zero value is found at the i-th position in the observed OR simulated
        array, the i-th value of the observed AND simulated array are removed before the
        computation.

    Returns
    -------
    float
        The mean normalized root mean square error.

    Examples
    --------

    >>> import HydroErr as he
    >>> import numpy as np

    >>> sim = np.array([5, 7, 9, 2, 4.5, 6.7])
    >>> obs = np.array([4.7, 6, 10, 2.5, 4, 7])
    >>> he.nrmse_mean(sim, obs)
    0.11725109740212526

    References
    ----------
    - Pontius, R.G., Thontteh, O., Chen, H., 2008. Components of information for multiple
      resolution comparison between maps that share a real variable. Environmental and Ecological
      Statistics 15(2) 111-142.

    """

    # Checking and cleaning the data
    
    simulated_array, observed_array = treat_values(
        simulated_array,
        observed_array,
        replace_nan=replace_nan,
        replace_inf=replace_inf,
        remove_neg=remove_neg,
        remove_zero=remove_zero
    )

    rmse_value = np.sqrt(np.mean((simulated_array - observed_array) ** 2))
    obs_mean = np.mean(observed_array)
    return rmse_value / obs_mean
Compute the mean normalized root mean square error between the simulated and observed data.

    .. image:: /pictures/NRMSE_Mean.png

    **Range:** 0 ≤ NRMSE < inf.

    **Notes:** This metric is the RMSE normalized by the mean of the observed time series (x).
    Normalizing allows comparison between data sets with different scales.

    Parameters
    ----------
    simulated_array: one dimensional ndarray
        An array of simulated data from the time series.

    observed_array: one dimensional ndarray
        An array of observed data from the time series.

    replace_nan: float, optional
        If given, indicates which value to replace NaN values with in the two arrays. If None, when
        a NaN value is found at the i-th position in the observed OR simulated array, the i-th value
        of the observed and simulated array are removed before the computation.

    replace_inf: float, optional
        If given, indicates which value to replace Inf values with in the two arrays. If None, when
        an inf value is found at the i-th position in the observed OR simulated array, the i-th
        value of the observed and simulated array are removed before the computation.

    remove_neg: boolean, optional
        If True, when a negative value is found at the i-th position in the observed OR simulated
        array, the i-th value of the observed AND simulated array are removed before the
        computation.

    remove_zero: boolean, optional
        If true, when a zero value is found at the i-th position in the observed OR simulated
        array, the i-th value of the observed AND simulated array are removed before the
        computation.

    Returns
    -------
    float
        The mean normalized root mean square error.

    Examples
    --------

    >>> import HydroErr as he
    >>> import numpy as np

    >>> sim = np.array([5, 7, 9, 2, 4.5, 6.7])
    >>> obs = np.array([4.7, 6, 10, 2.5, 4, 7])
    >>> he.nrmse_mean(sim, obs)
    0.11725109740212526

    References
    ----------
    - Pontius, R.G., Thontteh, O., Chen, H., 2008. Components of information for multiple
      resolution comparison between maps that share a real variable. Environmental and Ecological
      Statistics 15(2) 111-142.