How to use the lifetimes.utils._customer_lifetime_value function in Lifetimes

1          0        0  224
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    >>> print fitted_bg.predict(30, t['frequency'], t['recency'], t['T'])
    0    0.016053
    1    0.021171
    2    0.030461
    3    0.031686
    4    0.001607
    dtype: float64
    """
    t = fitted_bg.data.head()
    expected = np.array([0.016053, 0.021171, 0.030461, 0.031686, 0.001607])
    # discount_rate=0 means the clv will be the same as the predicted
    clv_d0 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=1, discount_rate=0.)
    assert_almost_equal(clv_d0.values, expected, decimal=5)
    # discount_rate=1 means the clv will halve over a period
    clv_d1 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=1, discount_rate=1.)
    assert_almost_equal(clv_d1.values, expected / 2., decimal=5)
    # time=2, discount_rate=0 means the clv will be twice the initial
    clv_t2_d0 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=2, discount_rate=0)
    assert_allclose(clv_t2_d0.values, expected * 2., rtol=0.1)
    # time=2, discount_rate=1 means the clv will be twice the initial
    clv_t2_d1 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=2, discount_rate=1.)
    assert_allclose(clv_t2_d1.values, expected / 2. + expected / 4., rtol=0.1)

1    0.021171
    2    0.030461
    3    0.031686
    4    0.001607
    dtype: float64
    """
    t = fitted_bg.data.head()
    expected = np.array([0.016053, 0.021171, 0.030461, 0.031686, 0.001607])
    # discount_rate=0 means the clv will be the same as the predicted
    clv_d0 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=1, discount_rate=0.)
    assert_almost_equal(clv_d0.values, expected, decimal=5)
    # discount_rate=1 means the clv will halve over a period
    clv_d1 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=1, discount_rate=1.)
    assert_almost_equal(clv_d1.values, expected / 2., decimal=5)
    # time=2, discount_rate=0 means the clv will be twice the initial
    clv_t2_d0 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=2, discount_rate=0)
    assert_allclose(clv_t2_d0.values, expected * 2., rtol=0.1)
    # time=2, discount_rate=1 means the clv will be twice the initial
    clv_t2_d1 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=2, discount_rate=1.)
    assert_allclose(clv_t2_d1.values, expected / 2. + expected / 4., rtol=0.1)

4    0.001607
    dtype: float64
    """
    t = fitted_bg.data.head()
    expected = np.array([0.016053, 0.021171, 0.030461, 0.031686, 0.001607])
    # discount_rate=0 means the clv will be the same as the predicted
    clv_d0 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=1, discount_rate=0.)
    assert_almost_equal(clv_d0.values, expected, decimal=5)
    # discount_rate=1 means the clv will halve over a period
    clv_d1 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=1, discount_rate=1.)
    assert_almost_equal(clv_d1.values, expected / 2., decimal=5)
    # time=2, discount_rate=0 means the clv will be twice the initial
    clv_t2_d0 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=2, discount_rate=0)
    assert_allclose(clv_t2_d0.values, expected * 2., rtol=0.1)
    # time=2, discount_rate=1 means the clv will be twice the initial
    clv_t2_d1 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=2, discount_rate=1.)
    assert_allclose(clv_t2_d1.values, expected / 2. + expected / 4., rtol=0.1)

4          2        9  183
    >>> print fitted_bg.predict(30, t['frequency'], t['recency'], t['T'])
    0    0.016053
    1    0.021171
    2    0.030461
    3    0.031686
    4    0.001607
    dtype: float64
    """
    t = fitted_bg.data.head()
    expected = np.array([0.016053, 0.021171, 0.030461, 0.031686, 0.001607])
    # discount_rate=0 means the clv will be the same as the predicted
    clv_d0 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=1, discount_rate=0.)
    assert_almost_equal(clv_d0.values, expected, decimal=5)
    # discount_rate=1 means the clv will halve over a period
    clv_d1 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=1, discount_rate=1.)
    assert_almost_equal(clv_d1.values, expected / 2., decimal=5)
    # time=2, discount_rate=0 means the clv will be twice the initial
    clv_t2_d0 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=2, discount_rate=0)
    assert_allclose(clv_t2_d0.values, expected * 2., rtol=0.1)
    # time=2, discount_rate=1 means the clv will be twice the initial
    clv_t2_d1 = utils._customer_lifetime_value(fitted_bg, t['frequency'], t['recency'], t['T'], monetary_value=pd.Series([1, 1, 1, 1, 1]), time=2, discount_rate=1.)
    assert_allclose(clv_t2_d1.values, expected / 2. + expected / 4., rtol=0.1)

discount_rate: float, optional
            the monthly adjusted discount rate. Default: 0.01
        freq: string, optional
            {"D", "H", "M", "W"} for day, hour, month, week. This represents what unit of time your T is measure in.

        Returns
        -------
        Series:
            Series object with customer ids as index and the estimated customer
            lifetime values as values
        """

        # use the Gamma-Gamma estimates for the monetary_values
        adjusted_monetary_value = self.conditional_expected_average_profit(frequency, monetary_value)

        return _customer_lifetime_value(
            transaction_prediction_model, frequency, recency, T, adjusted_monetary_value, time, discount_rate, freq=freq
        )