view = viewer.View(graphPDF)
# %%
graphCDF = distribution.drawCDF()
graphCDF.setTitle(
r"CDF of a normal distribution with parameters $\mu = 2.2$ and $\sigma = 0.6$"
)
view = viewer.View(graphCDF)
# %%
# A discrete distribution
# -----------------------
#
# We define a geometric distribution with parameter :math:`p = 0.7`.
p = 0.7
distribution = ot.Geometric(p)
print(distribution)
# %%
# We draw a sample of it :
size = 10
sample = distribution.getSample(size)
print(sample)
# %%
# We draw its PDF and its CDF :
graphPDF = distribution.drawPDF()
graphPDF.setTitle(r"PDF of a geometric distribution with parameter $p = 0.7$")
view = viewer.View(graphPDF)
# %%
distributionCollection.add(student) continuousDistributionCollection.add(student) triangular = ot.Triangular(-1.0, 2.0, 4.0) distributionCollection.add(triangular) continuousDistributionCollection.add(triangular) uniform = ot.Uniform(1.0, 2.0) distributionCollection.add(uniform) continuousDistributionCollection.add(uniform) weibull = ot.WeibullMin(1.0, 1.0, 2.0) distributionCollection.add(weibull) continuousDistributionCollection.add(weibull) geometric = ot.Geometric(0.5) distributionCollection.add(geometric) discreteDistributionCollection.add(geometric) binomial = ot.Binomial(10, 0.25) distributionCollection.add(binomial) discreteDistributionCollection.add(binomial) zipf = ot.ZipfMandelbrot(20, 5.25, 2.5) distributionCollection.add(zipf) discreteDistributionCollection.add(zipf) poisson = ot.Poisson(5.0) distributionCollection.add(poisson) discreteDistributionCollection.add(poisson)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Geometric().__class__.__name__ == 'Bernoulli':
distribution = ot.Bernoulli(0.7)
elif ot.Geometric().__class__.__name__ == 'Binomial':
distribution = ot.Binomial(5, 0.2)
elif ot.Geometric().__class__.__name__ == 'ComposedDistribution':
copula = ot.IndependentCopula(2)
marginals = [ot.Uniform(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, copula)
elif ot.Geometric().__class__.__name__ == 'CumulativeDistributionNetwork':
coll = [ot.Normal(2),ot.Dirichlet([0.5, 1.0, 1.5])]
distribution = ot.CumulativeDistributionNetwork(coll, ot.BipartiteGraph([[0,1], [0,1]]))
elif ot.Geometric().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
elif ot.Geometric().__class__.__name__ == 'KernelMixture':
kernel = ot.Uniform()
sample = ot.Normal().getSample(5)
bandwith = [1.0]
distribution = ot.KernelMixture(kernel, bandwith, sample)
elif ot.Geometric().__class__.__name__ == 'MaximumDistribution':
coll = [ot.Uniform(2.5, 3.5), ot.LogUniform(1.0, 1.2), ot.Triangular(2.0, 3.0, 4.0)]
distribution = ot.MaximumDistribution(coll)
elif ot.Geometric().__class__.__name__ == 'Multinomial':
distribution = ot.Multinomial(5, [0.2])
elif ot.Geometric().__class__.__name__ == 'RandomMixture':
coll = [ot.Triangular(0.0, 1.0, 5.0), ot.Uniform(-2.0, 2.0)]
weights = [0.8, 0.2]
cst = 3.0
distribution = ot.RandomMixture(coll, weights, cst)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.Geometric().__class__.__name__ == 'ComposedDistribution'):
correlation = ot.CorrelationMatrix(2)
correlation[1, 0] = 0.25
aCopula = ot.NormalCopula(correlation)
marginals = [ot.Normal(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, aCopula)
elif (ot.Geometric().__class__.__name__ == 'CumulativeDistributionNetwork'):
distribution = ot.CumulativeDistributionNetwork(
[ot.Normal(2), ot.Dirichlet([0.5, 1.0, 1.5])],
ot.BipartiteGraph([[0, 1], [0, 1]]))
else:
distribution = ot.Geometric()
dimension = distribution.getDimension()
if dimension <= 2:
if distribution.getDimension() == 1:
distribution.setDescription(['$x$'])
pdf_graph = distribution.drawPDF()
cdf_graph = distribution.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False)
else:
distribution.setDescription(['$x_1$', '$x_2$'])
pdf_graph = distribution.drawPDF()
fig = plt.figure(figsize=(10, 5))
import openturns as ot
ot.TESTPREAMBLE()
# QQPlot tests
size = 100
normal = ot.Normal(1)
sample = normal.getSample(size)
sample2 = ot.Gamma(3.0, 4.0, 0.0).getSample(size)
twoSamplesQQPlot = ot.VisualTest.DrawQQplot(sample, sample2)
print("twoSamplesQQPlot = ", twoSamplesQQPlot)
sampleDistributionQQPlot = ot.VisualTest.DrawQQplot(sample, normal)
print("sampleDistributionQQPlot = ", sampleDistributionQQPlot)
dist = ot.Geometric()
qq_plot = ot.VisualTest.DrawQQplot(dist.getSample(size), dist)
print("discrete QQPlot = ", qq_plot)
# HenryLine test
size = 100
normal = ot.Normal(1)
sample = normal.getSample(size)
henryPlot = ot.VisualTest.DrawHenryLine(sample)
print("HenryPlot = ", henryPlot)
# LinearModel tests
dimension = 2
R = ot.CorrelationMatrix(dimension)
R[0, 1] = 0.8
distribution = ot.Normal(
for j in range(i):
R[i, j] = (i + j + 1.0) / (2.0 * dim)
mean = [2.0] * dim
sigma = [3.0] * dim
distribution = ot.Normal(mean, sigma, R)
size = 100
sample = distribution.getSample(size)
sampleY = sample.getMarginal(0)
sampleZ = ot.Sample(size, 1)
for i in range(size):
sampleZ[i, 0] = sampleY[i, 0] * sampleY[i, 0]
discreteSample1 = ot.Poisson(0.1).getSample(size)
discreteSample2 = ot.Geometric(0.4).getSample(size)
# ChiSquared Independance test : test if two samples (of sizes not necessarily equal) are independant ?
# Care : discrete samples only
# H0 = independent samples
# p-value threshold : probability of the H0 reject zone : 0.10
# p-value : probability (test variable decision > test variable decision evaluated on the samples)
# Test = True <=> p-value > p-value threshold
print("ChiSquared=",
ot.HypothesisTest.ChiSquared(discreteSample1, discreteSample2, 0.10))
print("ChiSquared2=",
ot.HypothesisTest.ChiSquared(discreteSample1, discreteSample1, 0.10))
# Pearson Test : test if two gaussian samples are independent (based on the evaluation of the linear correlation coefficient)
# H0 : independent samples (linear correlation coefficient = 0)
# Test = True <=> independent samples (linear correlation coefficient = 0)
""" Create a geometric distribution =============================== """ # %% # In this example we are going to create a geometric distribution with parameter :math:`p = 0.7`. # %% from __future__ import print_function import openturns as ot import openturns.viewer as viewer from matplotlib import pylab as plt ot.Log.Show(ot.Log.NONE) distribution = ot.Geometric(0.7) print(distribution) # %% sample = distribution.getSample(10) print(sample) # %% graph = distribution.drawCDF() view = viewer.View(graph) plt.show()
"round": 1,
},
"ratio_shipping": {
"marg": ot.Normal(0.2, 0.07), # mean is 0.3
"corr": -0.05, # Negative correlation with CR
"bounds": [0.05, 0.4],
"round": 4,
},
"shipping_time": {
"marg": ot.Poisson(3.0), # mean is 3 days
"corr": -0.3, # The longer, the less CR
"bounds": [1, 14],
"round": 4,
},
"nb_rating": {
"marg": ot.Geometric(0.02), # mean is 50
"corr": 0.2, # The more the nb of rating, the better trust
"bounds": None,
"round": 0, # Already an integer (casted as double)
},
"avg_rating": {
"marg": ot.Triangular(1.0, 4.0, 5.0), # mode is 4.0
"corr": 0.25, # The better rating, the better the CR
"bounds": None,
"round": 2,
},
"nb_provider_rating": {
"marg": ot.Geometric(0.001), # mean is 1000
"corr": 0.08, # Weak positive correlation
"bounds": None,
"round": 0, # Already an integer (casted as double)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Geometric().__class__.__name__ == 'ComposedDistribution':
correlation = ot.CorrelationMatrix(2)
correlation[1, 0] = 0.25
aCopula = ot.NormalCopula(correlation)
marginals = [ot.Normal(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, aCopula)
elif ot.Geometric().__class__.__name__ == 'CumulativeDistributionNetwork':
distribution = ot.CumulativeDistributionNetwork([ot.Normal(2),ot.Dirichlet([0.5, 1.0, 1.5])], ot.BipartiteGraph([[0,1], [0,1]]))
elif ot.Geometric().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.Geometric()
dimension = distribution.getDimension()
if dimension == 1:
distribution.setDescription(['$x$'])
pdf_graph = distribution.drawPDF()
cdf_graph = distribution.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False)
elif dimension == 2:
distribution.setDescription(['$x_1$', '$x_2$'])
pdf_graph = distribution.drawPDF()
fig = plt.figure(figsize=(10, 5))
plt.suptitle(str(distribution))
ot.FittingTest.BestModelAIC(sample, distributions)
# %%
# Rank the continuous models wrt the AICc criteria:
ot.FittingTest.BestModelAICC(sample, distributions)
# %%
# **Discrete distributions**
# %%
# Create a sample from a discrete distribution
distribution = ot.Poisson(2.0)
sample = distribution.getSample(1000)
graph = ot.UserDefined(sample).drawCDF()
view = viewer.View(graph)
# %%
# Create the list of distribution estimators
distributions = [ot.Poisson(2.0), ot.Geometric(0.1)]
# %%
# Rank the discrete models wrt the ChiSquared p-values:
estimated_distribution, test_result = ot.FittingTest.BestModelChiSquared(
sample, distributions)
test_result
# %%
# Rank the discrete models wrt the BIC criteria:
ot.FittingTest.BestModelBIC(sample, distributions)
plt.show()
