Distribution Sampelr
Introduction
In this part, comparsion between actual sampler results and standard distribution is implemented, and all distribution sampler demo are exhibited as well.
Code can be found in pydpm/example/Sampler_Demo.py
The last default param ‘times=1' are skipped over.
Gamma
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.gamma(np.ones(1000)*4.5, 5)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(0, 100, 100), stats.gamma.pdf(np.linspace(0, 100, 100), 4.5, scale=5))
Plot
Standard gamma
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.standard_gamma(np.ones(1000)*4.5)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(0, 20, 100), stats.gamma.pdf(np.linspace(0, 20, 100), 4.5))
Plot
Dirichlet
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.dirichlet(np.ones(1000)*4.5)
plt.figure()
plt.hist(output, bins=20, density=True)
Plot
Beta
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.beta(np.ones(1000)*2, 5)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(0, 1, 100), stats.beta.pdf(np.linspace(0, 1, 100), 2, 5))
Plot
Normal
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.normal(np.ones(1000)*5, np.ones(1000)*2)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(-2, 13, 100), stats.norm.pdf(np.linspace(-2, 13, 100), 5, scale=2))
Plot
Standard Normal
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.standard_normal(1000)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(-3, 3, 100), stats.norm.pdf(np.linspace(-3, 3, 100)))
Plot
Uniform
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.uniform(np.ones(1000)*(-2), np.ones(1000)*5)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(-3, 6, 100), stats.uniform.pdf(np.linspace(-3, 6, 100), -2, 7))
Plot
Standard Uniform
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.standard_uniform(1000)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(-0.3, 1.3, 100), stats.uniform.pdf(np.linspace(-0.3, 1.3, 100)))
Plot
Binomial
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.binomial(np.ones(1000)*10, np.ones(1000)*0.5)
plt.figure()
plt.hist(output, bins=np.max(output)-np.min(output), density=True, range=(np.min(output)-0.5, np.max(output)-0.5))
Plot
Negative Binomial
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.negative_binomial(np.ones(1000)*10, 0.5)
plt.figure()
plt.hist(output, bins=np.max(output)-np.min(output), density=True, range=(np.min(output)-0.5, np.max(output)-0.5))
plt.scatter(np.arange(30), stats.nbinom._pmf(np.arange(30), 10, 0.5), c='orange', zorder=10)
Plot
Multinomial
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.multinomial(5, [0.8, 0.2], 1000)
plt.figure()
plt.hist(output[0], bins=15, density=True)
plt.title('multinomial(5, [0.8, 0.2])')
plt.show()
a = np.array([np.array([[i] * 6 for i in range(6)]).reshape(-1), np.array(list(range(6)) * 6)]).T
output = stats.multinomial(n=5, p=[0.8, 0.2]).pmf(a)
sns.heatmap(output.reshape(6, 6), annot=True)
plt.ylabel('number of the 1 kind(p=0.8)')
plt.xlabel('number of the 2 kind(p=0.2)')
plt.title('stats.multinomial(n=5, p=[0.8, 0.2])')
Plot
Poisson
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.poisson(np.ones(1000)*10)
plt.figure()
plt.hist(output, bins=22, density=True, range=(-0.5, 21.5))
plt.scatter(np.arange(20), stats.poisson.pmf(np.arange(20), 10), c='orange', zorder=10)
Plot
Cauchy
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.cauchy(np.ones(1000)*1, 0.5)
plt.figure()
plt.hist(output, bins=20, density=True, range=(-5, 7))
plt.plot(np.linspace(-5, 7, 100), stats.cauchy.pdf(np.linspace(-5, 7, 100), 1, 0.5))
Plot
Standard Cauchy
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.standard_cauchy(1000)
plt.figure()
plt.hist(output, bins=20, density=True, range=(-7, 7))
plt.plot(np.linspace(-7, 7, 100), stats.cauchy.pdf(np.linspace(-7, 7, 100)))
Plot
Chisquare
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.chisquare(np.ones(1000)*10)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(0, 30, 100), stats.chi2.pdf(np.linspace(0, 30, 100), 10))
Plot
Noncentral Chisquare
Demo
from pydpm._sampler import Basic_Sampler
output = sampler.noncentral_chisquare(np.ones(1000)*10, 5)
plt.figure()
plt.hist(output, bins=20, density=True)
Plot
Exponential
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
lam = 0.5
output = sampler.exponential(np.ones(1000)*lam)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(0.01, 4, 100), stats.expon.pdf(np.linspace(0.01, 4, 100), scale=0.5))
Plot
Standard Exponential
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.standard_exponential(1000)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(0.01, 8, 100), stats.expon.pdf(np.linspace(0.01, 8, 100)))
Plot
F
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.f(np.ones(1000)*10, 10)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(0, 8, 100), stats.f.pdf(np.linspace(0, 8, 100), 10, 10))
Plot
Noncentral F
Demo
from pydpm._sampler import Basic_Sampler
output = sampler.noncentral_f(np.ones(1000)*10, 10, 5)
plt.figure()
plt.hist(output, bins=20, density=True)
Plot
Geometric
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.geometric(np.ones(1000)*0.1)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.scatter(np.arange(50), stats.geom.pmf(np.arange(50), p=0.1), c='orange', zorder=10)
Plot
Gumbel
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.gumbel(np.ones(1000)*5, np.ones(1000)*2)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(0, 20, 100), stats.gumbel_r.pdf(np.linspace(0, 20, 100)+0.01, 5, scale=2))
Plot
Hypergeometric
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.hypergeometric(np.ones(1000)*5, 10, 10)
plt.figure()
plt.hist(output, bins=np.max(output)-np.min(output), density=True, range=(np.min(output)+0.5, np.max(output)+0.5))
plt.scatter(np.arange(10), stats.hypergeom(15, 5, 10).pmf(np.arange(10)), c='orange', zorder=10) # hypergeom(M, n, N), total, I, tiems
Plot
Laplace
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.laplace(np.ones(1000)*5, np.ones(1000)*2)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(-10, 20, 100), stats.laplace.pdf(np.linspace(-10, 20, 100), 5, scale=2))
Plot
Logistic
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.logistic(np.ones(1000)*5, np.ones(1000)*2)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(-10, 20, 100), stats.logistic.pdf(np.linspace(-10, 20, 100), 5, scale=2))
Plot
Power
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.power(np.ones(1000)*0.5)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(0, 1.5, 100), stats.powerlaw.pdf(np.linspace(0, 1.5, 100), 0.5))
Plot
Zipf
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.zipf(np.ones(1000)*1.1)
counter = Counter(output)
filter = np.array([[key, counter[key]] for key in counter.keys() if key < 50])
plt.figure()
plt.scatter(filter[:, 0], filter[:, 1] / 1000)
plt.plot(np.arange(1, 50), stats.zipf(1.1).pmf(np.arange(1, 50)))
Plot
Pareto
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.pareto(np.ones(1000) * 2, np.ones(1000) * 5)
plt.figure()
count, bins, _ = plt.hist(output, bins=50, density=True, range=(np.min(output), 100))
a, m = 2., 5. # shape and mode
fit = a * m ** a / bins ** (a + 1)
plt.plot(bins, max(count) * fit / max(fit), linewidth=2, color='r')
plt.title('pareto(2, 5)')
plt.show()
Plot
Rayleigh
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.rayleigh(np.ones(1000)*2.0)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(0, 8, 100), stats.rayleigh(scale=2).pdf(np.linspace(0, 8, 100)))
Plot
T
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.t(np.ones(1000)*2.0)
plt.figure()
plt.hist(output, bins=20, density=True, range=(-6, 6))
plt.plot(np.linspace(-6, 6, 100), stats.t(2).pdf(np.linspace(-6, 6, 100)))
Plot
Triangular
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.triangular(np.ones(1000)*0.0, 0.3, 1)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(0, 1, 100), stats.triang.pdf(np.linspace(0, 1, 100), 0.3))
Plot
Weibull
Demo
from pydpm._sampler import Basic_Sampler
import scipy.stats as stats
output = sampler.weibull(np.ones(1000)*4.5, 5)
plt.figure()
plt.hist(output, bins=20, density=True)
plt.plot(np.linspace(0, 10, 100), stats.weibull_min.pdf(np.linspace(0, 10, 100), 4.5, scale=5))
Plot
