def test_customer_lifetime_value_with_known_values(fitted_bg):
"""
>>> print fitted_bg
<lifetimes.BetaGeoFitter: fitted with 5000 subjects, r: 0.16, alpha: 1.86, a: 1.85, b: 3.18>
>>> t = fitted_bg.data.head()
>>> t
frequency recency T
0 0 0 298
1 0 0 224
2 6 142 292
3 0 0 147
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)
def test_customer_lifetime_value_with_known_values(fitted_bg):
"""
>>> print fitted_bg
<lifetimes.BetaGeoFitter: fitted with 5000 subjects, r: 0.16, alpha: 1.86, a: 1.85, b: 3.18>
>>> t = fitted_bg.data.head()
>>> t
frequency recency T
0 0 0 298
1 0 0 224
2 6 142 292
3 0 0 147
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)
def customer_lifetime_value(self,
transaction_prediction_model,
frequency,
recency,
T,
monetary_value,
time=12,
discount_rate=0.01):
"""
This method computes the average lifetime value for a group of one or more customers.
Parameters:
transaction_prediction_model: the model to predict future transactions, literature uses
pareto/ndb but we can also use a different model like bg
frequency: the frequency vector of customers' purchases (denoted x in literature).
recency: the recency vector of customers' purchases (denoted t_x in literature).
T: the vector of customers' age (time since first purchase)
monetary_value: the monetary value vector of customer's purchases (denoted m in literature).
time: the lifetime expected for the user in months. Default: 12
discount_rate: the monthly adjusted discount rate. Default: 0.01
Returns:
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)
def test_customer_lifetime_value_with_bgf(self):
from collections import OrderedDict
ggf = estimation.GammaGammaFitter()
ggf.params_ = OrderedDict({'p': 6.25, 'q': 3.74, 'v': 15.44})
bgf = estimation.BetaGeoFitter()
bgf.fit(cdnow_customers_with_monetary_value['frequency'],
cdnow_customers_with_monetary_value['recency'],
cdnow_customers_with_monetary_value['T'],
iterative_fitting=3)
ggf_clv = ggf.customer_lifetime_value(
bgf, cdnow_customers_with_monetary_value['frequency'],
cdnow_customers_with_monetary_value['recency'],
cdnow_customers_with_monetary_value['T'],
cdnow_customers_with_monetary_value['monetary_value'])
utils_clv = utils.customer_lifetime_value(
bgf, cdnow_customers_with_monetary_value['frequency'],
cdnow_customers_with_monetary_value['recency'],
cdnow_customers_with_monetary_value['T'],
ggf.conditional_expected_average_profit(
cdnow_customers_with_monetary_value['frequency'],
cdnow_customers_with_monetary_value['monetary_value']))
npt.assert_equal(ggf_clv.values, utils_clv.values)
def test_customer_lifetime_value_with_bgf(self):
from collections import OrderedDict
ggf = estimation.GammaGammaFitter()
ggf.params_ = OrderedDict({'p':6.25, 'q':3.74, 'v':15.44})
bgf = estimation.BetaGeoFitter()
bgf.fit(cdnow_customers_with_monetary_value['frequency'], cdnow_customers_with_monetary_value['recency'], cdnow_customers_with_monetary_value['T'], iterative_fitting=3)
ggf_clv = ggf.customer_lifetime_value(
bgf,
cdnow_customers_with_monetary_value['frequency'],
cdnow_customers_with_monetary_value['recency'],
cdnow_customers_with_monetary_value['T'],
cdnow_customers_with_monetary_value['monetary_value']
)
utils_clv = utils.customer_lifetime_value(
bgf,
cdnow_customers_with_monetary_value['frequency'],
cdnow_customers_with_monetary_value['recency'],
cdnow_customers_with_monetary_value['T'],
ggf.conditional_expected_average_profit(cdnow_customers_with_monetary_value['frequency'],cdnow_customers_with_monetary_value['monetary_value'])
)
npt.assert_equal(ggf_clv.values, utils_clv.values)
def customer_lifetime_value(self, transaction_prediction_model, frequency, recency, T, monetary_value, time=12, discount_rate=1):
"""
This method computes the average lifetime value for a group of one or more customers.
transaction_prediction_model: the model to predict future transactions, literature uses
pareto/ndb but we can also use a different model like bg
frequency: the frequency vector of customers' purchases (denoted x in literature).
recency: the recency vector of customers' purchases (denoted t_x in literature).
T: the vector of customers' age (time since first purchase)
monetary_value: the monetary value vector of customer's purchases (denoted m in literature).
time: the lifetime expected for the user in months. Default: 12
discount_rate: the monthly adjusted discount rate. Default: 1
Returns:
Series object with customer ids as index and the estimated customer lifetime values as values
"""
adjusted_monetary_value = self.conditional_expected_average_profit(frequency, monetary_value) # use the Gamma-Gamma estimates for the monetary_values
return customer_lifetime_value(transaction_prediction_model, frequency, recency, T, adjusted_monetary_value, time, discount_rate)
