def test_fit_with_and_without_weights(self, cdnow_customers):
original_dataset_with_weights = cdnow_customers.copy()
original_dataset_with_weights = original_dataset_with_weights.groupby(
['frequency', 'recency', 'T']).size()
original_dataset_with_weights = original_dataset_with_weights.reset_index(
)
original_dataset_with_weights = original_dataset_with_weights.rename(
columns={0: 'weights'})
pnbd_noweights = estimation.ParetoNBDFitter()
pnbd_noweights.fit(
cdnow_customers['frequency'],
cdnow_customers['recency'],
cdnow_customers['T'],
)
pnbd = estimation.ParetoNBDFitter()
pnbd.fit(
original_dataset_with_weights['frequency'],
original_dataset_with_weights['recency'],
original_dataset_with_weights['T'],
original_dataset_with_weights['weights'],
)
npt.assert_array_almost_equal(
np.array(pnbd_noweights._unload_params('r', 'alpha', 's', 'beta')),
np.array(pnbd._unload_params('r', 'alpha', 's', 'beta')),
decimal=2)
def test_fit_with_index(self, cdnow_customers):
ptf = estimation.ParetoNBDFitter()
index = range(len(cdnow_customers), 0, -1)
ptf.fit(cdnow_customers['frequency'],
cdnow_customers['recency'],
cdnow_customers['T'],
index=index)
assert (ptf.data.index == index).all() == True
ptf = estimation.ParetoNBDFitter()
ptf.fit(cdnow_customers['frequency'],
cdnow_customers['recency'],
cdnow_customers['T'],
index=None)
assert (ptf.data.index == index).all() == False
def test_conditional_probability_alive_is_between_0_and_1(self, cdnow_customers):
ptf = estimation.ParetoNBDFitter()
ptf.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'])
for freq in np.arange(0, 100, 10.):
for recency in np.arange(0, 100, 10.):
for t in np.arange(recency, 100, 10.):
assert 0.0 <= ptf.conditional_probability_alive(freq, recency, t) <= 1.0
def test_conditional_probability_alive_is_between_0_and_1(self):
ptf = estimation.ParetoNBDFitter()
ptf.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'])
for i in range(0, 100, 10):
for j in range(0, 100, 10):
for k in range(j, 100, 10):
assert 0 <= ptf.conditional_probability_alive(i, j, k) <= 1.0
def test_conditional_probability_alive_matrix(self, cdnow_customers):
ptf = estimation.ParetoNBDFitter()
ptf.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'])
Z = ptf.conditional_probability_alive_matrix()
max_t = int(ptf.data['T'].max())
for t_x in range(Z.shape[0]):
for x in range(Z.shape[1]):
assert Z[t_x][x] == ptf.conditional_probability_alive(x, t_x, max_t)
def test_expectation_returns_same_value_as_R_BTYD(self, cdnow_customers):
""" From https://cran.r-project.org/web/packages/BTYD/BTYD.pdf """
ptf = estimation.ParetoNBDFitter()
ptf.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'], tol=1e-6)
expected = np.array([0.00000000, 0.05077821, 0.09916088, 0.14542507, 0.18979930,
0.23247466, 0.27361274, 0.31335159, 0.35181024, 0.38909211])
actual = ptf.expected_number_of_purchases_up_to_time(range(10))
npt.assert_allclose(expected, actual, atol=0.01)
def test_overflow_error(self):
ptf = estimation.ParetoNBDFitter()
params = np.array([10.465, 7.98565181e-03, 3.0516, 2.820])
freq = np.array([400., 500., 500.])
rec = np.array([5., 1., 4.])
age = np.array([6., 37., 37.])
assert all([r < 0 and not np.isinf(r) and not pd.isnull(r)
for r in ptf._log_A_0(params, freq, rec, age)])
def test_conditional_probability_alive_overflow_error(self):
ptf = estimation.ParetoNBDFitter()
ptf.params_ = OrderedDict(
zip(['r', 'alpha', 's', 'beta'],
[10.465, 7.98565181e-03, 3.0516, 2.820]))
freq = np.array([400., 500., 500.])
rec = np.array([5., 1., 4.])
age = np.array([6., 37., 37.])
assert all([r <= 1 and r >= 0 and not np.isinf(r) and not pd.isnull(r)
for r in ptf.conditional_probability_alive(freq, rec, age)])
def test_params_out_is_close_to_Hardie_paper(self, cdnow_customers):
ptf = estimation.ParetoNBDFitter()
ptf.fit(cdnow_customers['frequency'],
cdnow_customers['recency'],
cdnow_customers['T'],
iterative_fitting=3)
expected = np.array([0.553, 10.578, 0.606, 11.669])
npt.assert_array_almost_equal(
expected,
np.array(ptf._unload_params('r', 'alpha', 's', 'beta')),
decimal=3)
def test_conditional_expectation_returns_same_value_as_R_BTYD(self, cdnow_customers):
""" From https://cran.r-project.org/web/packages/BTYD/vignettes/BTYD-walkthrough.pdf """
ptf = estimation.ParetoNBDFitter()
ptf.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'])
x = 26.00
t_x = 30.86
T = 31
t = 52
expected = 25.46
actual = ptf.conditional_expected_number_of_purchases_up_to_time(t, x, t_x, T)
assert abs(expected - actual) < 0.01
def test_conditional_probability_alive(self, cdnow_customers):
"""
Target taken from page 8,
https://cran.r-project.org/web/packages/BTYD/vignettes/BTYD-walkthrough.pdf
"""
ptf = estimation.ParetoNBDFitter()
ptf.params_ = OrderedDict(
zip(['r', 'alpha', 's', 'beta'],
[0.5534, 10.5802, 0.6061, 11.6562]))
p_alive = ptf.conditional_probability_alive(26.00, 30.86, 31.00)
assert abs(p_alive - 0.9979) < 0.001
def test_conditional_expectation_underflow(self):
""" Test a pair of inputs for the ParetoNBD ptf.conditional_expected_number_of_purchases_up_to_time().
For a small change in the input, the result shouldn't change dramatically -- however, if the
function doesn't guard against numeric underflow, this change in input will result in an
underflow error.
"""
ptf = estimation.ParetoNBDFitter()
alpha = 10.58
beta = 11.67
r = 0.55
s = 0.61
ptf.params_ = OrderedDict({'alpha':alpha, 'beta':beta, 'r':r, 's':s})
# small change in inputs
left = ptf.conditional_expected_number_of_purchases_up_to_time(10, 132, 200, 200) # 6.2060517889632418
right = ptf.conditional_expected_number_of_purchases_up_to_time(10, 133, 200, 200) # 6.2528722475748113
assert abs(left - right) < 0.05
def test_conditional_probability_of_n_purchases_up_to_time_is_between_0_and_1(
self, cdnow_customers):
"""
Due to the large parameter space we take a random subset.
"""
ptf = estimation.ParetoNBDFitter()
ptf.fit(cdnow_customers['frequency'], cdnow_customers['recency'],
cdnow_customers['T'])
for freq in np.random.choice(100, 5):
for recency in np.random.choice(100, 5):
for age in recency + np.random.choice(100, 5):
for t in np.random.choice(100, 5):
for n in np.random.choice(10, 5):
assert (
0.0 <= ptf.
conditional_probability_of_n_purchases_up_to_time(
n, t, freq, recency, age) <= 1.0)
def test_Ex_estimation_and_error(self):
ptf = estimation.ParetoNBDFitter()
frequency = [0, 0, 0, 1, 1, 0, 2, 5, 6, 6, 0, 10]
recency = [0, 0, 0, 1, 10, 0, 8, 8, 9, 9, 0, 10]
T = [10] * len(frequency)
ptf.fit(frequency, recency, T, initial_params=[0.5, 2, 0.5, 0.5])
t = 100
C = [[0.02, 0, 0, 0], [0, 1.0, 0, 0], [0, 0, 0.03, 0.0],
[0, 0, 0, 2.0]]
Ex = ptf.expected_number_of_purchases_up_to_time(t)
Ex_err = ptf.expected_number_of_purchases_up_to_time_error(t, C)
assert 25 > Ex > 15
assert Ex_err > 0
compressed_frequency = [0, 1, 1, 2, 5, 6, 10]
compressed_recency = [0, 1, 10, 8, 8, 9, 10]
compressed_T = [10, 10, 10, 10, 10, 10, 10]
ptf.fit(compressed_frequency,
compressed_recency,
compressed_T,
initial_params=[0.5, 2, 0.5, 0.5])
t = 100
C = [[0.02, 0, 0, 0], [0, 1.0, 0, 0], [0, 0, 0.03, 0.0],
[0, 0, 0, 2.0]]
Ex2 = ptf.expected_number_of_purchases_up_to_time(t)
Ex2_err = ptf.expected_number_of_purchases_up_to_time_error(t, C)
assert 25 > Ex > 15
assert Ex_err > 0
ptf.fit(cdnow_customers['frequency'], cdnow_customers['recency'],
cdnow_customers['T'])
Ex = ptf.expected_number_of_purchases_up_to_time(t)
Ex_err = ptf.expected_number_of_purchases_up_to_time_error(t, C)
assert Ex > 0
assert Ex_err > 0
def test_conditional_probability_of_n_purchases_up_to_time_adds_up_to_1(
self, cdnow_customers):
"""
Due to the large parameter space we take a random subset. We also restrict our limits to keep the number of
values of n for which the probability needs to be calculated to a sane level.
"""
ptf = estimation.ParetoNBDFitter()
ptf.fit(cdnow_customers['frequency'], cdnow_customers['recency'],
cdnow_customers['T'])
for freq in np.random.choice(10, 5):
for recency in np.random.choice(9, 5):
for age in np.random.choice(np.arange(recency, 10, 1), 5):
for t in 1 + np.random.choice(9, 5):
npt.assert_almost_equal(np.sum([
ptf.
conditional_probability_of_n_purchases_up_to_time(
n, t, freq, recency, age)
for n in np.arange(0, 20, 1)
]),
1.0,
decimal=2)