def logistic_mixture_norm_test():
xscale = Scale(-50, 50)
return LogisticMixture(
components=[Logistic(-40, 1, xscale),
Logistic(50, 10, xscale)],
probs=[0.5, 0.5],
)
def normalized_logistic_mixture():
return LogisticMixture(
components=[
Logistic(loc=0.15, s=0.037034005, scale=Scale(0, 1)),
Logistic(loc=0.85, s=0.032395907, scale=Scale(0, 1)),
],
probs=[0.6, 0.4],
)
def logistic_mixture():
return LogisticMixture(
components=[
Logistic(loc=10000, scale=1000),
Logistic(loc=100000, scale=10000)
],
probs=[0.8, 0.2],
)
def logistic_mixture_p_overlapping():
xscale = three_sd_scale(4000000.035555004, 200000.02)
return LogisticMixture(
components=[
Logistic(4000000.035555004, 200000.02, xscale),
Logistic(4000000.0329152746, 200000.0, xscale),
],
probs=[0.5, 0.5],
)
def logistic_mixture_p_uneven():
xscale = Scale(-10, 20)
return LogisticMixture(
components=[
Logistic(loc=10, s=3, scale=xscale),
Logistic(loc=5, s=5, scale=xscale),
],
probs=[1.8629593e-29, 1.0],
)
def logistic_mixture10():
xscale = Scale(-20, 40)
return LogisticMixture(
components=[
Logistic(loc=15, s=2.3658268, scale=xscale),
Logistic(loc=5, s=2.3658268, scale=xscale),
],
probs=[0.5, 0.5],
)
def logistic_mixture():
xscale = Scale(0, 150000)
return LogisticMixture(
components=[
Logistic(loc=10000, s=1000, scale=xscale),
Logistic(loc=100000, s=10000, scale=xscale),
],
probs=[0.8, 0.2],
)
def logistic_mixture15():
xscale = Scale(-10, 40)
return LogisticMixture(
components=[
Logistic(loc=10, s=3.658268, scale=xscale),
Logistic(loc=20, s=3.658268, scale=xscale),
],
probs=[0.5, 0.5],
)
def smooth_logistic_mixture():
xscale = Scale(1, 1000000.0)
return LogisticMixture(
components=[
Logistic(loc=400000, s=100000, scale=xscale),
Logistic(loc=700000, s=50000, scale=xscale),
],
probs=[0.8, 0.2],
)
def truncated_logistic_mixture():
xscale = Scale(5000, 120000)
return LogisticMixture(
components=[
Truncate(
Logistic(loc=10000, s=1000, scale=xscale), floor=5000, ceiling=500000
),
Truncate(
Logistic(loc=100000, s=10000, scale=xscale), floor=5000, ceiling=500000
),
],
probs=[0.8, 0.2],
)
def test_percentiles_from_mixture():
xscale = Scale(-1, 4)
mixture = LogisticMixture(
components=[
Logistic(loc=1, s=0.1, scale=xscale),
Logistic(loc=2, s=0.1, scale=xscale),
],
probs=[0.5, 0.5],
)
conditions = mixture.percentiles(percentiles=[0.1, 0.5, 0.9])
for condition in conditions:
if condition.max == 0.5:
assert condition.p == pytest.approx(1.5, rel=0.01)
return conditions
def get_true_scale_logistic(self, normalized_dist: Logistic) -> Logistic:
"""
Convert a normalized logistic distribution to a logistic on
the true scale of the question.
:param normalized_dist: normalized logistic distribution
:return: logistic distribution on the true scale of the question
"""
scale_loc = (normalized_dist.loc * self.question_range_width +
self.question_range["min"])
true_scale = normalized_dist.scale * self.question_range_width
return Logistic(scale_loc, true_scale)
def easyLogistic(loc, scale):
return Logistic(loc, scale, three_sd_scale(loc, scale))
