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#! /usr/bin/env python
# %%
import openturns as ot
import openturns.testing as ott
import os
# %%
ot.TESTPREAMBLE()
# Instantiate one distribution object
distribution = ot.Binomial(15, 0.7)
print("Distribution ", repr(distribution))
print("Distribution ", distribution)
# Is this distribution elliptical ?
print("Elliptical = ", distribution.isElliptical())
# Is this distribution continuous ?
print("Continuous = ", distribution.isContinuous())
# Test for realization of distribution
oneRealization = distribution.getRealization()
print("oneRealization=", repr(oneRealization))
# Define a point
point = ot.Point(distribution.getDimension(), 5.0)
print("Point= ", repr(point))
# PDF value
PDF = distribution.computePDF(point)
print("pdf =%.6f" % PDF)
# derivative of the PDF with regards the parameters of the distribution
CDF = distribution.computeCDF(point)
print("cdf=%.6f" % CDF)
# quantile
quantile = distribution.computeQuantile(0.95)
print("quantile=", repr(quantile))
print("cdf(quantile)=%.6f" % distribution.computeCDF(quantile))
print("entropy=%.6f" % distribution.computeEntropy())
mean = distribution.getMean()
print("mean=", repr(mean))
standardDeviation = distribution.getStandardDeviation()
print("standard deviation=", repr(standardDeviation))
skewness = distribution.getSkewness()
print("skewness=", repr(skewness))
kurtosis = distribution.getKurtosis()
print("kurtosis=", repr(kurtosis))
covariance = distribution.getCovariance()
print("covariance=", repr(covariance))
parameters = distribution.getParametersCollection()
print("parameters=", repr(parameters))
print("Standard representative=", distribution.getStandardRepresentative())
# Confidence interval
alpha = 0.05
bounds = distribution.computeBilateralConfidenceInterval(1 - alpha)
print("%.2f%% bilateral confidence interval" % ((1 - alpha) * 100), " =", bounds)
# %%
# check survival at upper bound
distribution = ot.Binomial(10, 1.0)
assert distribution.computeCDF(10.0) == 1.0
assert distribution.computeComplementaryCDF(10.0) == 0.0
assert distribution.computeSurvivalFunction(10.0) == 0.0
# negative quantile bug
distribution = ot.Binomial(3, 0.5)
assert distribution.computeScalarQuantile(0.9, True) == 0
# %%
print("Check on dataset")
separator = ","
path = os.path.join(os.path.dirname(__file__), "t_Binomial_std.csv")
sample = ot.Sample.ImportFromTextFile(path, separator)
rtol = 1.0e-12
atol = ot.SpecFunc.MinScalar
sample_size = sample.getSize()
for i in range(sample_size):
x, n, pr, expected_pdf, expected_cdfp, expected_cdfq = sample[i]
x = int(x)
n = int(n)
distribution = ot.Binomial(n, pr)
computed_p = distribution.computePDF(x)
computed_cdf = distribution.computeCDF(x)
computed_ccdf = distribution.computeComplementaryCDF(x)
computed_surv = distribution.computeSurvivalFunction(x)
print(
f"row = {i}/{sample_size}, x = {x}, n = {n}, pr = {pr}, "
f"P(X = x) = {expected_pdf}, CDF = {expected_cdfp}, Compl. CDF = {expected_cdfq}"
)
# Check PDF
print(
f" computePDF. Computed = {computed_p:.11e}, expected = {expected_pdf:.11e}"
)
ott.assert_almost_equal(computed_p, expected_pdf, rtol, atol)
# Check CDF
print(
f" computeCDF. Computed = {computed_cdf:.11e}, expected = {expected_cdfp:.11e}"
)
ott.assert_almost_equal(computed_cdf, expected_cdfp, rtol, atol)
# Check complementary CDF
print(
f" computeComplementaryCDF. Computed = {computed_ccdf:.11e}, "
f"expected = {expected_cdfq:.11e}"
)
ott.assert_almost_equal(computed_ccdf, expected_cdfq, rtol, atol)
# Check Survival
print(
f" computeSurvivalFunction. Computed = {computed_surv:.11e}, "
f"expected = {computed_ccdf:.11e}"
)
ott.assert_almost_equal(computed_surv, computed_ccdf, rtol, atol)
# Check quantile
if pr == 0.0 and x < n:
# The function is not invertible
# for this particular input.
continue
elif expected_cdfp < expected_cdfq:
computed_x = int(distribution.computeQuantile(computed_cdf)[0])
cdfXM1 = distribution.computeCDF(computed_x - 1)
cdfX = distribution.computeCDF(computed_x)
print(
f" computeQuantile (A). Computed X = {computed_x}, "
f"F(X - 1) = {cdfXM1:.7e}, F(X) = {cdfX:.7e}"
)
if computed_cdf == 0.0:
assert computed_x == 0.0
else:
assert cdfXM1 < computed_cdf and computed_cdf <= cdfX
else:
computed_x = int(distribution.computeQuantile(computed_ccdf, True)[0])
print(f" computeQuantile (B). Computed X = {computed_x}, expected = {x}")
assert x == computed_x
if i > 0:
ott.assert_almost_equal(
distribution.computeScalarQuantile(expected_cdfp), x, 0.0, 1.0
) # Can be off by 1 unit
# %%
# quantile bug
alpha = 0.05
beta = 0.05
for n in range(59, 100):
d = ot.Binomial(n, alpha)
k = d.computeQuantile(beta)[0]
p1 = d.computeCDF(k - 1)
p2 = d.computeCDF(k)
ok = p1 < beta <= p2
print(f"n={n} k={k:.0f} p(k-1)={p1:.4f} p(k)={p2:.4f} ok={ok}")
assert ok
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(distribution)
validation.run()
# Corner cases
# 2147483647 is the maximum integer.
# Values greater than this are not doubles anymore.
binomial = ot.Binomial()
N = 2147483647
binomial.setN(N)
binomial.setP(1.0 / N)
computed = binomial.computePDF(1.0)
expected = 0.3678794
ott.assert_almost_equal(computed, expected, 1.0e-6, 0.0)
computed = binomial.computePDF(2.0)
expected = 0.1839397
ott.assert_almost_equal(computed, expected, 1.0e-6, 0.0)
# Extreme inputs
binomial = ot.Binomial()
binomial.setN(9999)
binomial.setP(0.5)
computed = binomial.computePDF(4999.0)
expected = 0.0079786461393821558191
ott.assert_almost_equal(computed, expected, 1.0e-7, 0.0)
# Check pdf for values of P closer to 1
binomial = ot.Binomial()
binomial.setN(2)
binomial.setP(0.9999)
computed = binomial.computePDF(1.0)
expected = 1.999799999999779835e-04
ott.assert_almost_equal(computed, expected, 1e-12, 0.0)
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