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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _find_statistics(X, y, variogram_function, variogram_model_parameters, coordinates_type):
 """Calculates variogram fit statistics. Returns the delta, sigma, and epsilon values for the variogram fit. These arrays are used for statistics calculations. Parameters X: ndarray float array [n_samples, n_dim], the input array of coordinates y: ndarray float array [n_samples], the input array of measurement values variogram_function: callable function that will be called to evaluate variogram model variogram_model_parameters: list user-specified parameters for variogram model coordinates_type: str type of coordinates in X array, can be 'euclidean' for standard rectangular coordinates or 'geographic' if the coordinates are lat/lon Returns ------- delta: ndarray residuals between observed values and kriged estimates for those values sigma: ndarray mean error in kriging estimates epsilon: ndarray residuals normalized by their mean error """


    delta = np.zeros(y.shape)
    sigma = np.zeros(y.shape)

    for i in range(y.shape[0]):

        # skip the first value in the kriging problem
        if i == 0:
            continue

        else:
            k, ss = _krige(X[:i, :], y[:i], X[i, :], variogram_function,
                           variogram_model_parameters, coordinates_type)

            # if the estimation error is zero, it's probably because
            # the evaluation point X[i, :] is really close to one of the
            # kriging system points in X[:i, :]...
            # in the case of zero estimation error, the results are not stored
            if np.absolute(ss) < eps:
                continue

            delta[i] = y[i] - k
            sigma[i] = np.sqrt(ss)

    # only use non-zero entries in these arrays... sigma is used to pull out
    # non-zero entries in both cases because it is guaranteed to be positive,
    # whereas delta can be either positive or negative
    delta = delta[sigma > eps]
    sigma = sigma[sigma > eps]
    epsilon = delta/sigma

    return delta, sigma, epsilon