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MBBEFD cumulative loss distribution should be used in your MBBEFD example, not G(x) exposure curve. #3

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MBBEFD cumulative loss distribution should be used in your MBBEFD example, not G(x) exposure curve. #3

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edit to use the MBBEFD cumulative distribution function rather than G…
hdavid333 May 3, 2025
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16 changes: 8 additions & 8 deletions docs/2_user_guides/2_x_re_pricing.rst
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Expand Up @@ -323,7 +323,7 @@ Property Risk Exposure Rating

Property risk exposure rating differs from casualty in part because the severity distribution varies with each risk (location). Rather than a single ground-up severity curve per class, there is a size of loss distribution normalized by property total insured value (TIV).

We start by introducing the Swiss Re severity curves, :cite:t:`Bernegger1997` using a moments-matched beta distribution. The function ``G`` defines the MBBEFD distribution, parameterized by ``c``.
We start by introducing the Swiss Re severity curves, :cite:t:`Bernegger1997` using a moments-matched beta distribution. The function ``F`` defines the MBBEFD distribution, parameterized by ``c``.

.. ipython:: python
:okwarning:
Expand All @@ -339,10 +339,10 @@ We start by introducing the Swiss Re severity curves, :cite:t:`Bernegger1997` us
def bg(c):
return np.exp((0.78 + 0.12*c)*c)

def G(x, c):
def F(x, c):
b = bb(c)
g = bg(c)
return np.log(((g - 1) * b + (1 - g * b) * b**x) / (1 - b)) / np.log(g * b)
return np.where(x == 1 , 1 , 1-(1-b)/((g-1)*b**(1-x)+(1-g*b)))


Here are the base curves, compare Figure 4.2 in :cite:t:`Bernegger1997`. The curve ``c=5`` is close to the Lloyd's curve (scale).
Expand All @@ -355,13 +355,13 @@ Here are the base curves, compare Figure 4.2 in :cite:t:`Bernegger1997`. The cur
ans = []
ps = np.linspace(0,1,101)
for c in [0, 1, 2, 3, 4, 5]:
gs = G(ps, c)
ax.plot(ps, gs, label=f'c={c}')
ans.append([c, *xsden_to_meancv(ps[1:], np.diff(gs))])
fs = F(ps, c)
ax.plot(ps, fs, label=f'c={c}')
ans.append([c, *xsden_to_meancv(ps[1:], np.diff(fs))])
ax.legend(loc='lower right');
@savefig prop_ch1.png scale=20
ax.set(xlabel='Proportion of limit', ylabel='Proportion of expected loss',
title='Swiss Re property scales');
ax.set(xlabel='Loss degree x', ylabel='Probablity of X <= x',
title='MBBDF Distribution');

Next, approximate these curves with a beta distribution to make them easier for us to use in ``aggregate``. Here are the parameters and fit graphs for each curve.

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