def calculate_severity_distribution(elt, grid_size=2**14, max_loss_factor=5):
""" This function calculates the severity distribution or the distribution
of the size of losses, given that an event has occurred
----------
elt : pandas dataframe containing ELT
Returns
-------
severity_distribution
"""
max_loss = _max_loss(elt, max_loss_factor=max_loss_factor)
loss_thresholds = numpy.linspace(0, max_loss, num=grid_size + 1)
probability = {}
CEP = {}
for threshold in loss_thresholds:
probability[threshold] = 1 - beta.cdf(threshold / elt['ExpValue'],
elt['alpha'], elt['beta'])
probability[threshold] = np.nan_to_num(probability[threshold])
CEP[threshold] = sum(
elt['Rate'] * probability[threshold]) / ELT(elt).get_lambda()
severity_distribution = pd.DataFrame(CEP.items(),
columns=['threshold', 'CEP'])
severity_density_function = severity_distribution.copy(deep=True)
severity_density_function['shift_CEP'] = severity_density_function[
'CEP'].shift(1)
severity_density_function = severity_density_function[1:]
severity_density_function['CEP'] = severity_density_function[
'shift_CEP'] - severity_density_function['CEP']
severity_density_function.drop('shift_CEP', axis=1, inplace=True)
return severity_distribution, severity_density_function
def test_invalid_elt_columns_raises_value_error():
""" Test invalid ELT data raises value error """
bad_elt_data = [{
"PeriodId": 526,
"Loss": 44536,
"StdDevI": 7441,
"StdDevC": 22090,
"ExpValue": 300000,
"Rate": 0.000729
}]
with pytest.raises(ValueError):
ELT(bad_elt_data)
def calculate_aep_curve(elt, grid_size=2**14, max_loss_factor=5):
""" This function calculates the OEP of a given ELT
----------
elt : pandas dataframe containing PLT
grid_size: grid size used for ep calculations
max_loss_factor: factor used to extimate max loss
Returns
-------
EPCurve :
exceedance probability curve
"""
elt_lambda = ELT(elt).get_lambda()
max_loss = _max_loss(elt, max_loss_factor)
dx = max_loss / grid_size
xx = np.arange(1, grid_size + 1) * dx
severity_distribution, severity_density_function = calculate_severity_distribution(
elt, grid_size, max_loss_factor)
elt['dx'] = dx / elt['ExpValue']
elt['xx'] = ''
elt['FX'] = ''
elt['FX2'] = ''
fx2 = [0] * grid_size
for index, row in elt.iterrows():
row['xx'] = np.true_divide(xx, row['ExpValue'])
row['FX'] = beta.cdf(row['xx'], row['alpha'], row['beta'])
row['FX2'] = beta.cdf(row['xx'][0] - row['dx'] / 2, row['alpha'],
row['beta'])
cdf2 = beta.cdf(row['xx'][:-1] + row['dx'] / 2, row['alpha'],
row['beta'])
cdf1 = beta.cdf(row['xx'][:-1] - row['dx'] / 2, row['alpha'],
row['beta'])
row['FX2'] = np.insert(cdf2 - cdf1, 0, row['FX2'])
fx2 = fx2 + (row['Rate'] / elt_lambda) * row['FX2']
elt.at[index] = row
fx_hat = fft(fx2)
fs_hat = numpy.exp(-elt_lambda * (1 - fx_hat))
fs = numpy.real(ifft(fs_hat, norm="forward") / grid_size)
fs_cum = numpy.cumsum(fs)
severity_density_function['AEP'] = 1 - fs_cum
aep = severity_density_function.rename(columns={
'AEP': 'Probability',
'threshold': 'Loss'
})
return ep_curve.EPCurve(aep, ep_type=ep_curve.EPType.AEP)
def calculate_frequency_distribution(elt):
""" This function calculates the frequency distribution or the probability of having
exactly n occurences in a year
----------
elt : pandas dataframe containing ELT
Returns
-------
frequency_distribution
"""
elt_lambda = ELT(elt).get_lambda()
max_freq = max(3, 1 + _poisson_inv(1 - 1 / 20000, elt_lambda))
frequency_distribution = [
_poisson_pdf(n, elt_lambda) for n in range(0, max_freq + 1)
]
return frequency_distribution
def group_elts(elt1, elt2=None):
""" This function groups two elts together
Parameters
----------
elt1 : pandas dataframe containing ELT
elt2 : pandas dataframe containing elt
Returns
-------
elt :
A pandas dataframe containing a elt
"""
if elt2 is None:
grouped_elt = elt1.elt
else:
grouped_elt = pd.concat([elt1.elt, elt2.elt], axis=0)
elt_unique = grouped_elt[[
'EventId', 'Rate', 'Loss', 'StdDevI', 'StdDevC', 'ExpValue'
]].loc[~grouped_elt.duplicated(subset='EventId', keep=False), :]
elt_matches = grouped_elt[[
'EventId', 'Rate', 'Loss', 'StdDevI', 'StdDevC', 'ExpValue'
]].loc[grouped_elt.duplicated(subset='EventId', keep=False), :]
elt_matches = elt_matches.groupby(['EventId', 'Rate']).agg({
'Loss':
'sum',
'StdDevC':
'sum',
'ExpValue':
'sum',
'StdDevI':
lambda x: np.sqrt((x * x).sum())
}).reset_index()
concatenated_elt = pd.concat([elt_unique,
elt_matches]).reset_index(drop=True)
return ELT(concatenated_elt)
def calculate_oep_curve(elt, grid_size=2**14, max_loss_factor=5):
""" This function calculates the OEP of a given ELT
----------
elt : pandas dataframe containing PLT
grid_size: grid size used for ep calculations
max_loss_factor: factor used to extimate max loss
Returns
-------
EPCurve :
exceedance probability curve
"""
elt_lambda = ELT(elt).get_lambda()
severity_distribution, severity_density_function = calculate_severity_distribution(
elt, grid_size, max_loss_factor)
severity_distribution['OEP'] = 1 - numpy.exp(
-elt_lambda * severity_distribution['CEP'])
oep = severity_distribution.rename(columns={
'OEP': 'Probability',
'threshold': 'Loss'
})
return ep_curve.EPCurve(oep, ep_type=ep_curve.EPType.OEP)
def test_get_aal():
""" Test Get AAL from ELT """
my_elt = ELT(DATA)
assert my_elt.get_aal() == pytest.approx(151.30, 0.1)
def test_get_cv():
""" Test Get CV from ELT """
my_elt = ELT(DATA)
assert my_elt.get_covvar() == pytest.approx(31.64, 0.1)
def test_get_standard_deviation():
""" Test Get Standard Deviation from ELT """
my_elt = ELT(DATA)
assert my_elt.get_standard_deviation() == pytest.approx(4791, 0.1)