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pepicellopepicello
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FMT: fix travis tests (#90)
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‎empyrical/stats.py

Lines changed: 51 additions & 50 deletions
Original file line numberDiff line numberDiff line change
@@ -409,7 +409,7 @@ def expected_max_drawdown(mu, sigma, t, gbm=False):
409409
"""
410410
Determines the expected maximum drawdown of a brownian motion,
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given drift and diffusion
412-
412+
413413
If a geometric Brownian motion with stochastic differential equation
414414
dS(t) = Mu0 * S(t) * dt + Sigma0 * S(t) * dW(t) ,
415415
it converts to the form here by Ito's Lemma with X(t) = log(S(t)) such that
@@ -433,7 +433,8 @@ def expected_max_drawdown(mu, sigma, t, gbm=False):
433433
434434
Note
435435
-----
436-
See http://www.cs.rpi.edu/~magdon/ps/journal/drawdown_journal.pdf for more details.
436+
See http://www.cs.rpi.edu/~magdon/ps/journal/drawdown_journal.pdf
437+
for more details.
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"""
438439

439440
if gbm:
@@ -442,33 +443,33 @@ def expected_max_drawdown(mu, sigma, t, gbm=False):
442443
new_mu = mu
443444

444445
def emdd_qp(x):
445-
""" Return value for Q functions based on lookup table, for positive drifts"""
446-
A = [ 0.0005, 0.001, 0.0015, 0.002, 0.0025, 0.005,
447-
0.0075, 0.01, 0.0125, 0.015, 0.0175, 0.02,
448-
0.0225, 0.025, 0.0275, 0.03, 0.0325, 0.035,
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0.0375, 0.04, 0.0425, 0.045, 0.0475, 0.05,
450-
0.055, 0.06, 0.065, 0.07, 0.075, 0.08,
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0.085, 0.09, 0.095, 0.1, 0.15, 0.2,
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0.25, 0.3, 0.35, 0.4, 0.45, 0.5,
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1.0, 1.5, 2.0, 2.5, 3.0, 3.5,
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4.0, 4.5, 5.0, 10.0, 15.0, 20.0,
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25.0, 30.0, 35.0, 40.0, 45.0, 50.0,
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100.0, 150.0, 200.0, 250.0, 300.0, 350.0,
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400.0, 450.0, 500.0, 1000.0, 1500.0, 2000.0,
458-
2500.0, 3000.0, 3500.0, 4000.0, 4500.0, 5000.0 ]
459-
B = [ 0.01969, 0.027694, 0.033789, 0.038896, 0.043372, 0.060721,
460-
0.073808, 0.084693, 0.094171, 0.102651, 0.110375, 0.117503,
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0.124142, 0.130374, 0.136259, 0.141842, 0.147162, 0.152249,
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0.157127, 0.161817, 0.166337, 0.170702, 0.174924, 0.179015,
463-
0.186842, 0.194248, 0.201287, 0.207999, 0.214421, 0.220581,
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0.226505, 0.232212, 0.237722, 0.24305, 0.288719, 0.325071,
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0.355581, 0.382016, 0.405415, 0.426452, 0.445588, 0.463159,
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0.588642, 0.668992, 0.72854, 0.775976, 0.815456, 0.849298,
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0.878933, 0.905305, 0.92907, 1.088998, 1.184918, 1.253794,
468-
1.307607, 1.351794, 1.389289, 1.42186, 1.450654, 1.476457,
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1.647113, 1.747485, 1.818873, 1.874323, 1.919671, 1.958037,
470-
1.991288, 2.02063, 2.046885, 2.219765, 2.320983, 2.392826,
471-
2.448562, 2.494109, 2.532622, 2.565985, 2.595416, 2.621743 ]
446+
""" Q function based on lookup table, for positive drifts """
447+
A = [0.0005, 0.001, 0.0015, 0.002, 0.0025, 0.005,
448+
0.0075, 0.01, 0.0125, 0.015, 0.0175, 0.02,
449+
0.0225, 0.025, 0.0275, 0.03, 0.0325, 0.035,
450+
0.0375, 0.04, 0.0425, 0.045, 0.0475, 0.05,
451+
0.055, 0.06, 0.065, 0.07, 0.075, 0.08,
452+
0.085, 0.09, 0.095, 0.1, 0.15, 0.2,
453+
0.25, 0.3, 0.35, 0.4, 0.45, 0.5,
454+
1.0, 1.5, 2.0, 2.5, 3.0, 3.5,
455+
4.0, 4.5, 5.0, 10.0, 15.0, 20.0,
456+
25.0, 30.0, 35.0, 40.0, 45.0, 50.0,
457+
100.0, 150.0, 200.0, 250.0, 300.0, 350.0,
458+
400.0, 450.0, 500.0, 1000.0, 1500.0, 2000.0,
459+
2500.0, 3000.0, 3500.0, 4000.0, 4500.0, 5000.0]
460+
B = [0.01969, 0.027694, 0.033789, 0.038896, 0.043372, 0.060721,
461+
0.073808, 0.084693, 0.094171, 0.102651, 0.110375, 0.117503,
462+
0.124142, 0.130374, 0.136259, 0.141842, 0.147162, 0.152249,
463+
0.157127, 0.161817, 0.166337, 0.170702, 0.174924, 0.179015,
464+
0.186842, 0.194248, 0.201287, 0.207999, 0.214421, 0.220581,
465+
0.226505, 0.232212, 0.237722, 0.24305, 0.288719, 0.325071,
466+
0.355581, 0.382016, 0.405415, 0.426452, 0.445588, 0.463159,
467+
0.588642, 0.668992, 0.72854, 0.775976, 0.815456, 0.849298,
468+
0.878933, 0.905305, 0.92907, 1.088998, 1.184918, 1.253794,
469+
1.307607, 1.351794, 1.389289, 1.42186, 1.450654, 1.476457,
470+
1.647113, 1.747485, 1.818873, 1.874323, 1.919671, 1.958037,
471+
1.991288, 2.02063, 2.046885, 2.219765, 2.320983, 2.392826,
472+
2.448562, 2.494109, 2.532622, 2.565985, 2.595416, 2.621743]
472473
if x > 5000:
473474
return 0.25 * np.log(x) + 0.49088
474475
elif x < 0.0005:
@@ -477,27 +478,27 @@ def emdd_qp(x):
477478
return interpolate.interp1d(A, B)([x])[0]
478479

479480
def emdd_qn(x):
480-
""" Return value for Q functions based on lookup table, for negative drifts"""
481-
A = [ 0.0005, 0.001, 0.0015, 0.002, 0.0025, 0.005,
482-
0.0075, 0.01, 0.0125, 0.015, 0.0175, 0.02,
483-
0.0225, 0.025, 0.0275, 0.03, 0.0325, 0.035,
484-
0.0375, 0.04, 0.0425, 0.045, 0.0475, 0.05,
485-
0.055, 0.06, 0.065, 0.07, 0.075, 0.08,
486-
0.085, 0.09, 0.095, 0.1, 0.15, 0.2,
487-
0.25, 0.3, 0.35, 0.4, 0.45, 0.5,
488-
0.75, 1.0, 1.25, 1.5, 1.75, 2.0,
489-
2.25, 2.5, 2.75, 3.0, 3.25, 3.5,
490-
3.75, 4.0, 4.25, 4.5, 4.75, 5.0 ]
491-
B = [ 0.019965, 0.028394, 0.034874, 0.040369, 0.045256, 0.064633,
492-
0.079746, 0.092708, 0.104259, 0.114814, 0.124608, 0.133772,
493-
0.142429, 0.150739, 0.158565, 0.166229, 0.173756, 0.180793,
494-
0.187739, 0.194489, 0.201094, 0.207572, 0.213877, 0.220056,
495-
0.231797, 0.243374, 0.254585, 0.265472, 0.27607, 0.286406,
496-
0.296507, 0.306393, 0.316066, 0.325586, 0.413136, 0.491599,
497-
0.564333, 0.633007, 0.698849, 0.762455, 0.824484, 0.884593,
498-
1.17202, 1.44552, 1.70936, 1.97074, 2.22742, 2.48396,
499-
2.73676, 2.99094, 3.24354, 3.49252, 3.74294, 3.99519,
500-
4.24274, 4.49238, 4.73859, 4.99043, 5.24083, 5.49882 ]
481+
""" Q function based on lookup table, for negative drifts """
482+
A = [0.0005, 0.001, 0.0015, 0.002, 0.0025, 0.005,
483+
0.0075, 0.01, 0.0125, 0.015, 0.0175, 0.02,
484+
0.0225, 0.025, 0.0275, 0.03, 0.0325, 0.035,
485+
0.0375, 0.04, 0.0425, 0.045, 0.0475, 0.05,
486+
0.055, 0.06, 0.065, 0.07, 0.075, 0.08,
487+
0.085, 0.09, 0.095, 0.1, 0.15, 0.2,
488+
0.25, 0.3, 0.35, 0.4, 0.45, 0.5,
489+
0.75, 1.0, 1.25, 1.5, 1.75, 2.0,
490+
2.25, 2.5, 2.75, 3.0, 3.25, 3.5,
491+
3.75, 4.0, 4.25, 4.5, 4.75, 5.0]
492+
B = [0.019965, 0.028394, 0.034874, 0.040369, 0.045256, 0.064633,
493+
0.079746, 0.092708, 0.104259, 0.114814, 0.124608, 0.133772,
494+
0.142429, 0.150739, 0.158565, 0.166229, 0.173756, 0.180793,
495+
0.187739, 0.194489, 0.201094, 0.207572, 0.213877, 0.220056,
496+
0.231797, 0.243374, 0.254585, 0.265472, 0.27607, 0.286406,
497+
0.296507, 0.306393, 0.316066, 0.325586, 0.413136, 0.491599,
498+
0.564333, 0.633007, 0.698849, 0.762455, 0.824484, 0.884593,
499+
1.17202, 1.44552, 1.70936, 1.97074, 2.22742, 2.48396,
500+
2.73676, 2.99094, 3.24354, 3.49252, 3.74294, 3.99519,
501+
4.24274, 4.49238, 4.73859, 4.99043, 5.24083, 5.49882]
501502
if x > 5:
502503
return x + 0.5
503504
elif x < 0.0005:

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