def _propagate_distr_impl(self, distr0, time_delta, assume_distr=False):
if not isinstance(distr0, distrs.LogNormalDistr) and not assume_distr:
raise ValueError('Do not know how to propagate a distribution that is not log-normal')
# Note: the sum of two independent log-normal distributions is only approximately log-normal
mean = np.log(distr0.mean) + (self._pct_drift - .5 * npu.col([self._pct_cov[i, i] for i in range(self.process_dim)])) * time_delta
cov = distr0.cov + time_delta * self._pct_cov
return distrs.LogNormalDistr(mean_of_log=mean, cov_of_log=cov)
def test_log_normal_distr(self):
rnd.random_state(np.random.RandomState(seed=42), force=True)
std_log_normal_1d = distrs.LogNormalDistr(dim=1)
npt.assert_almost_equal(std_log_normal_1d.mean, [[ 1.6487213]])
npt.assert_almost_equal(std_log_normal_1d.cov, [[ 4.6707743]])
npt.assert_almost_equal(std_log_normal_1d.vol, [[ 2.1611974]])
sample = std_log_normal_1d.sample(size=1)
self.assertEqual(np.shape(sample), (1, 1))
npt.assert_almost_equal(sample, [[ 1.6433127]])
sample = std_log_normal_1d.sample(size=10)
self.assertEqual(np.shape(sample), (10, 1))
npt.assert_almost_equal(sample, [
[ 0.87086849],
[ 1.91111824],
[ 4.58609939],
[ 0.79124045],
[ 0.79125344],
[ 4.85113557],
[ 2.15423297],
[ 0.62533086],
[ 1.72040554],
[ 0.62912979]])
std_log_normal_2d = distrs.LogNormalDistr(dim=2)
npt.assert_almost_equal(std_log_normal_2d.mean, [
[ 1.6487213],
[ 1.6487213]])
npt.assert_almost_equal(std_log_normal_2d.cov, [
[ 4.6707743, 0. ],
[ 0. , 4.6707743]])
npt.assert_almost_equal(std_log_normal_2d.vol, [
[ 2.1611974, 0. ],
[ 0. , 2.1611974]])
sample = std_log_normal_2d.sample(size=10)
self.assertEqual(np.shape(sample), (10, 2))
npt.assert_almost_equal(sample, [
[ 0.62767689, 1.27374614],
[ 0.14759544, 0.17818769],
[ 0.5699039 , 0.36318929],
[ 1.36922835, 0.40332037],
[ 0.2435815 , 4.33035173],
[ 0.79789657, 1.06986043],
[ 0.24056903, 0.58019982],
[ 1.11730841, 0.31632232],
[ 1.45600738, 0.54846123],
[ 0.74699727, 0.54787583]])
sd1=.4; sd2=.4; cor=-.5
log_normal_2d = distrs.LogNormalDistr(mean_of_log=[1., 1.3], cov_of_log=stats.make_cov_2d(sd1=sd1, sd2=sd2, cor=cor))
npt.assert_almost_equal(log_normal_2d.mean_of_log, npu.col(1., 1.3))
npt.assert_almost_equal(log_normal_2d.cov_of_log, [[sd1*sd1, cor*sd1*sd2], [cor*sd1*sd2, sd2*sd2]])
npt.assert_almost_equal(log_normal_2d.vol_of_log, [[sd1, 0.], [cor*sd2, np.sqrt(1.-cor*cor)*sd2]])
npt.assert_almost_equal(log_normal_2d.mean, [[ 2.9446796], [ 3.9749016]])
npt.assert_almost_equal(log_normal_2d.cov, [[ 1.5045366, -0.8999087], [-0.8999087, 2.7414445]])
npt.assert_almost_equal(log_normal_2d.vol, [[ 1.2265956, 0. ], [-0.7336637, 1.484312 ]])
sample = log_normal_2d.sample(size=10)
self.assertEqual(np.shape(sample), (10, 2))
npt.assert_almost_equal(sample, [
[ 1.42711164, 6.95143797],
[ 4.62238496, 2.99848502],
[ 4.32618186, 2.50643161],
[ 4.10913455, 1.42691268],
[ 2.94320341, 4.55346303],
[ 2.50304159, 3.80468825],
[ 2.24476532, 2.45957906],
[ 3.18112082, 2.60781028],
[ 2.01884543, 5.66848303],
[ 5.34174201, 2.12565878]])
log_normal_2d = distrs.LogNormalDistr(mean_of_log=[1., 1.3], vol_of_log=stats.make_vol_2d(sd1=sd1, sd2=sd2, cor=cor))
npt.assert_almost_equal(log_normal_2d.mean_of_log, npu.col(1., 1.3))
npt.assert_almost_equal(log_normal_2d.cov_of_log, [[sd1*sd1, cor*sd1*sd2], [cor*sd1*sd2, sd2*sd2]])
npt.assert_almost_equal(log_normal_2d.vol_of_log, [[sd1, 0.], [cor*sd2, np.sqrt(1.-cor*cor)*sd2]])
npt.assert_almost_equal(log_normal_2d.mean, npu.col(2.9446796, 3.9749016))
npt.assert_almost_equal(log_normal_2d.cov, [[ 1.5045366, -0.8999087], [-0.8999087, 2.7414445]])
npt.assert_almost_equal(log_normal_2d.vol, [[ 1.2265956, 0. ], [-0.7336637, 1.484312 ]])
sample = log_normal_2d.sample(size=10)
self.assertEqual(np.shape(sample), (10, 2))
npt.assert_almost_equal(sample, [
[ 2.71288329, 2.80448293],
[ 2.70285608, 5.57387658],
[ 1.66454464, 4.28346127],
[ 3.23285936, 3.52238521],
[ 1.76160691, 4.67441442],
[ 2.32343609, 2.75776026],
[ 4.8398479 , 2.85230385],
[ 1.67494888, 5.78583855],
[ 2.06409776, 5.58431178],
[ 3.6537541 , 3.15441508]])