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Improve accuracy of kde() invcdf estimates #124637

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Merged
merged 2 commits into from
Sep 27, 2024
Merged

Improve accuracy of kde() invcdf estimates #124637

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2365fed
Improve accuracy of quartic_invcdf_estimate
rhettinger Sep 26, 2024
d8ee745
Improve triweight invcdf estimate
rhettinger Sep 27, 2024
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8 changes: 7 additions & 1 deletion Lib/statistics.py
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Original file line number Diff line number Diff line change
Expand Up @@ -870,9 +870,12 @@ def f_inv(y):
return f_inv

def _quartic_invcdf_estimate(p):
# A handrolled piecewise approximation. There is no magic here.
sign, p = (1.0, p) if p <= 1/2 else (-1.0, 1.0 - p)
if p < 0.0106:
return ((2.0 * p) ** 0.3838 - 1.0) * sign
x = (2.0 * p) ** 0.4258865685331 - 1.0
if p >= 0.004 < 0.499:
if p < 0.499:
x += 0.026818732 * sin(7.101753784 * p + 2.73230839482953)
return x * sign

Expand All @@ -886,8 +889,11 @@ def quartic_kernel():
return pdf, cdf, invcdf, support

def _triweight_invcdf_estimate(p):
# A handrolled piecewise approximation. There is no magic here.
sign, p = (1.0, p) if p <= 1/2 else (-1.0, 1.0 - p)
x = (2.0 * p) ** 0.3400218741872791 - 1.0
if 0.00001 < p < 0.499:
x -= 0.033 * sin(1.07 * tau * (p - 0.035))
return x * sign

@register('triweight')
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