Estimating mean and relative size of a sample of a population

statistics.py

def estimate_mean(sample, values, weights=None):
    """Estimates the average value of a set of elements based on the given
    sample.

    Parameters
    ----------
    sample : iterable
       Iterable of objects.

    values : function
       This function takes elements from ``sample`` as inputs and must return
       a :class:`float` representing the value of the element.

    weights : function
       This function takes elements from ``sample`` as inputs and must return
       a :class:`float` representing the weight of the element. If this is
       not provided, then it is assumed to be the constant function.

    Returns
    -------
    float
       An estimate of the mean of the values of all elements.

    Examples
    --------
    Estimating the mean of twice the node indices in the wheel graph on ten
    vertices::

       >>> import networkx as nx
       >>> G = nx.wheel_graph(10)
       >>> sample = uniform_independent_node_sample(G, size=20)
       >>> estimate_mean(sample, values=lambda x: 2 * x)
       8.9000000000000004

    Estimating the mean of the node labels on a graph given a large number of
    samples::

        >>> import networkx as nx
        >>> G = nx.wheel_graph(10)
        >>> N = 10000
        >>> sample = list(nx.uniform_independent_node_sample(G, size=N))
        >>> nx.estimate_mean(sample, lambda v: v)
        ???

    Estimating the mean of the node labels on a graph given a large number of
    samples, weighted according to degree::

        >>> import networkx as nx
        >>> G = nx.wheel_graph(10)
        >>> N = 10000
        >>> sample = list(nx.uniform_independent_node_sample(G, size=N))
        >>> nx.estimate_mean(sample, values, weights=G.degree)
        ???

    """
    if weights is None:
        weights = lambda x: 1
    up = sum(values(v) / weights(v) for v in sample)
    down = sum(1 / weights(v) for v in sample)
    return up / down


def estimate_relative_size(sample, labeled, weights=None):
    """Estimates the fraction of labeled objects given a sample of the entire
    population.

    Parameters
    ----------
    sample : iterable
       Iterable of objects.

    labeled : Boolean function
       This function takes elements from ``sample`` as inputs and must return
       ``True`` if and only if the element is labeled.

    weights : function
       This function takes elements from ``sample`` as inputs and must return
       a :class:`float` representing the weight of the element.

    Returns
    -------
    int
       An estimate of the fraction of labeled elements.

    Examples
    --------
    Estimate the fraction of labeled elements in the wheel graph on ten
    vertices, where the first five nodes are labeled::

        >>> import networkx as nx
        >>> G = nx.wheel_graph(10)
        >>> is_labeled = lambda v: v in range(5)
        >>> estimate_relative_size(S, labeled=is_labeled, weights=G.degree)
        0.50679999999999814

    """
    values = lambda s: 1 if labeled(s) else 0
    return estimate_mean(sample, values, weights)