    
    Args:
        predictions (distribution): a batch of distribution predictions.
        reduction (str): the method to aggregate the results across the batch. Can be 'none', 'mean', 'sum', 'median', 'min', or 'max'. 
        resolution (int): the number of discretization bins, where higher resolution increases estimation accuracy but also requires more memory/compute.
    
    Returns:
        tensor with shape [batch_size] or []: The computed mean, when reduction is 'none' the shape is [batch_size], otherwise the shape is []. 
    """
    quantiles = _implicit_quantiles(resolution) 