À quoi ressemblent toutes les distributions disponibles dans scipy.stats?
Visualisation scipy.stats distributions
Un histogramme peut être composé de le scipy.stats variable aléatoire normale pour voir à quoi ressemble la distribution.
% matplotlib inline
import pandas as pd
import scipy.stats as stats
d = stats.norm()
rv = d.rvs(100000)
pd.Series(rv).hist(bins=32, normed=True)
À quoi ressemblent les autres distributions?
Visualisation de toutes les distributions scipy.stats
Sur la base de la liste des distributions de scipy.stats , tracées ci-dessous sont les histogramme s et PDF s de chaque variable aléatoire continue . Le code utilisé pour générer chaque distribution est en bas . Remarque: Les constantes de forme proviennent des exemples des pages de documentation de distribution de scipy.stats.
alpha(a=3.57, loc=0.00, scale=1.00)
anglit(loc=0.00, scale=1.00)
arcsine(loc=0.00, scale=1.00)
beta(a=2.31, loc=0.00, scale=1.00, b=0.63)
betaprime(a=5.00, loc=0.00, scale=1.00, b=6.00)
bradford(loc=0.00, c=0.30, scale=1.00)
burr(loc=0.00, c=10.50, scale=1.00, d=4.30)
cauchy(loc=0.00, scale=1.00)
chi(df=78.00, loc=0.00, scale=1.00)
chi2(df=55.00, loc=0.00, scale=1.00)
cosine(loc=0.00, scale=1.00)
dgamma(a=1.10, loc=0.00, scale=1.00)
dweibull(loc=0.00, c=2.07, scale=1.00)
erlang(a=2.00, loc=0.00, scale=1.00)
expon(loc=0.00, scale=1.00)
exponnorm(loc=0.00, K=1.50, scale=1.00)
exponpow(loc=0.00, scale=1.00, b=2.70)
exponweib(a=2.89, loc=0.00, c=1.95, scale=1.00)
f(loc=0.00, dfn=29.00, scale=1.00, dfd=18.00)
fatiguelife(loc=0.00, c=29.00, scale=1.00)
fisk(loc=0.00, c=3.09, scale=1.00)
foldcauchy(loc=0.00, c=4.72, scale=1.00)
foldnorm(loc=0.00, c=1.95, scale=1.00)
frechet_l(loc=0.00, c=3.63, scale=1.00)
frechet_r(loc=0.00, c=1.89, scale=1.00)
gamma(a=1.99, loc=0.00, scale=1.00)
gausshyper(a=13.80, loc=0.00, c=2.51, scale=1.00, b=3.12, z=5.18)
genexpon(a=9.13, loc=0.00, c=3.28, scale=1.00, b=16.20)
genextreme(loc=0.00, c=-0.10, scale=1.00)
gengamma(a=4.42, loc=0.00, c=-3.12, scale=1.00)
genhalflogistic(loc=0.00, c=0.77, scale=1.00)
genlogistic(loc=0.00, c=0.41, scale=1.00)
gennorm(loc=0.00, beta=1.30, scale=1.00)
genpareto(loc=0.00, c=0.10, scale=1.00)
gilbrat(loc=0.00, scale=1.00)
gompertz(loc=0.00, c=0.95, scale=1.00)
gumbel_l(loc=0.00, scale=1.00)
gumbel_r(loc=0.00, scale=1.00)
halfcauchy(loc=0.00, scale=1.00)
halfgennorm(loc=0.00, beta=0.68, scale=1.00)
halflogistic(loc=0.00, scale=1.00)
halfnorm(loc=0.00, scale=1.00)
hypsecant(loc=0.00, scale=1.00)
invgamma(a=4.07, loc=0.00, scale=1.00)
invgauss(mu=0.14, loc=0.00, scale=1.00)
invweibull(loc=0.00, c=10.60, scale=1.00)
johnsonsb(a=4.32, loc=0.00, scale=1.00, b=3.18)
johnsonsu(a=2.55, loc=0.00, scale=1.00, b=2.25)
ksone(loc=0.00, scale=1.00, n=1000.00)
kstwobign(loc=0.00, scale=1.00)
laplace(loc=0.00, scale=1.00)
levy(loc=0.00, scale=1.00)
levy_l(loc=0.00, scale=1.00)
loggamma(loc=0.00, c=0.41, scale=1.00)
logistic(loc=0.00, scale=1.00)
loglaplace(loc=0.00, c=3.25, scale=1.00)
lognorm(loc=0.00, s=0.95, scale=1.00)
lomax(loc=0.00, c=1.88, scale=1.00)
maxwell(loc=0.00, scale=1.00)
mielke(loc=0.00, s=3.60, scale=1.00, k=10.40)
nakagami(loc=0.00, scale=1.00, nu=4.97)
ncf(loc=0.00, dfn=27.00, nc=0.42, dfd=27.00, scale=1.00)
nct(df=14.00, loc=0.00, scale=1.00, nc=0.24)
ncx2(df=21.00, loc=0.00, scale=1.00, nc=1.06)
norm(loc=0.00, scale=1.00)
Pareto(loc=0.00, scale=1.00, b=2.62)
pearson3(loc=0.00, skew=0.10, scale=1.00)
powerlaw(a=1.66, loc=0.00, scale=1.00)
powerlognorm(loc=0.00, s=0.45, scale=1.00, c=2.14)
powernorm(loc=0.00, c=4.45, scale=1.00)
rayleigh(loc=0.00, scale=1.00)
rdist(loc=0.00, c=0.90, scale=1.00)
recipinvgauss(mu=0.63, loc=0.00, scale=1.00)
reciprocal(a=0.01, loc=0.00, scale=1.00, b=1.01)
rice(loc=0.00, scale=1.00, b=0.78)
semicircular(loc=0.00, scale=1.00)
t(df=2.74, loc=0.00, scale=1.00)
triang(loc=0.00, c=0.16, scale=1.00)
truncexpon(loc=0.00, scale=1.00, b=4.69)
truncnorm(a=0.10, loc=0.00, scale=1.00, b=2.00)
tukeylambda(loc=0.00, scale=1.00, lam=3.13)
uniform(loc=0.00, scale=1.00)
vonmises(loc=0.00, scale=1.00, kappa=3.99)
vonmises_line(loc=0.00, scale=1.00, kappa=3.99)
wald(loc=0.00, scale=1.00)
weibull_max(loc=0.00, c=2.87, scale=1.00)
weibull_min(loc=0.00, c=1.79, scale=1.00)
wrapcauchy(loc=0.00, c=0.03, scale=1.00)
Code de génération
Voici le Jupyter Notebook utilisé pour générer les tracés.
%matplotlib inline
import io
import numpy as np
import pandas as pd
import scipy.stats as stats
import matplotlib
import matplotlib.pyplot as plt
matplotlib.rcParams['figure.figsize'] = (16.0, 14.0)
matplotlib.style.use('ggplot')
# Distributions to check, shape constants were taken from the examples on the scipy.stats distribution documentation pages.
DISTRIBUTIONS = [
stats.alpha(a=3.57, loc=0.0, scale=1.0), stats.anglit(loc=0.0, scale=1.0),
stats.arcsine(loc=0.0, scale=1.0), stats.beta(a=2.31, b=0.627, loc=0.0, scale=1.0),
stats.betaprime(a=5, b=6, loc=0.0, scale=1.0), stats.bradford(c=0.299, loc=0.0, scale=1.0),
stats.burr(c=10.5, d=4.3, loc=0.0, scale=1.0), stats.cauchy(loc=0.0, scale=1.0),
stats.chi(df=78, loc=0.0, scale=1.0), stats.chi2(df=55, loc=0.0, scale=1.0),
stats.cosine(loc=0.0, scale=1.0), stats.dgamma(a=1.1, loc=0.0, scale=1.0),
stats.dweibull(c=2.07, loc=0.0, scale=1.0), stats.erlang(a=2, loc=0.0, scale=1.0),
stats.expon(loc=0.0, scale=1.0), stats.exponnorm(K=1.5, loc=0.0, scale=1.0),
stats.exponweib(a=2.89, c=1.95, loc=0.0, scale=1.0), stats.exponpow(b=2.7, loc=0.0, scale=1.0),
stats.f(dfn=29, dfd=18, loc=0.0, scale=1.0), stats.fatiguelife(c=29, loc=0.0, scale=1.0),
stats.fisk(c=3.09, loc=0.0, scale=1.0), stats.foldcauchy(c=4.72, loc=0.0, scale=1.0),
stats.foldnorm(c=1.95, loc=0.0, scale=1.0), stats.frechet_r(c=1.89, loc=0.0, scale=1.0),
stats.frechet_l(c=3.63, loc=0.0, scale=1.0), stats.genlogistic(c=0.412, loc=0.0, scale=1.0),
stats.genpareto(c=0.1, loc=0.0, scale=1.0), stats.gennorm(beta=1.3, loc=0.0, scale=1.0),
stats.genexpon(a=9.13, b=16.2, c=3.28, loc=0.0, scale=1.0), stats.genextreme(c=-0.1, loc=0.0, scale=1.0),
stats.gausshyper(a=13.8, b=3.12, c=2.51, z=5.18, loc=0.0, scale=1.0), stats.gamma(a=1.99, loc=0.0, scale=1.0),
stats.gengamma(a=4.42, c=-3.12, loc=0.0, scale=1.0), stats.genhalflogistic(c=0.773, loc=0.0, scale=1.0),
stats.gilbrat(loc=0.0, scale=1.0), stats.gompertz(c=0.947, loc=0.0, scale=1.0),
stats.gumbel_r(loc=0.0, scale=1.0), stats.gumbel_l(loc=0.0, scale=1.0),
stats.halfcauchy(loc=0.0, scale=1.0), stats.halflogistic(loc=0.0, scale=1.0),
stats.halfnorm(loc=0.0, scale=1.0), stats.halfgennorm(beta=0.675, loc=0.0, scale=1.0),
stats.hypsecant(loc=0.0, scale=1.0), stats.invgamma(a=4.07, loc=0.0, scale=1.0),
stats.invgauss(mu=0.145, loc=0.0, scale=1.0), stats.invweibull(c=10.6, loc=0.0, scale=1.0),
stats.johnsonsb(a=4.32, b=3.18, loc=0.0, scale=1.0), stats.johnsonsu(a=2.55, b=2.25, loc=0.0, scale=1.0),
stats.ksone(n=1e+03, loc=0.0, scale=1.0), stats.kstwobign(loc=0.0, scale=1.0),
stats.laplace(loc=0.0, scale=1.0), stats.levy(loc=0.0, scale=1.0),
stats.levy_l(loc=0.0, scale=1.0), stats.levy_stable(alpha=0.357, beta=-0.675, loc=0.0, scale=1.0),
stats.logistic(loc=0.0, scale=1.0), stats.loggamma(c=0.414, loc=0.0, scale=1.0),
stats.loglaplace(c=3.25, loc=0.0, scale=1.0), stats.lognorm(s=0.954, loc=0.0, scale=1.0),
stats.lomax(c=1.88, loc=0.0, scale=1.0), stats.maxwell(loc=0.0, scale=1.0),
stats.mielke(k=10.4, s=3.6, loc=0.0, scale=1.0), stats.nakagami(nu=4.97, loc=0.0, scale=1.0),
stats.ncx2(df=21, nc=1.06, loc=0.0, scale=1.0), stats.ncf(dfn=27, dfd=27, nc=0.416, loc=0.0, scale=1.0),
stats.nct(df=14, nc=0.24, loc=0.0, scale=1.0), stats.norm(loc=0.0, scale=1.0),
stats.Pareto(b=2.62, loc=0.0, scale=1.0), stats.pearson3(skew=0.1, loc=0.0, scale=1.0),
stats.powerlaw(a=1.66, loc=0.0, scale=1.0), stats.powerlognorm(c=2.14, s=0.446, loc=0.0, scale=1.0),
stats.powernorm(c=4.45, loc=0.0, scale=1.0), stats.rdist(c=0.9, loc=0.0, scale=1.0),
stats.reciprocal(a=0.00623, b=1.01, loc=0.0, scale=1.0), stats.rayleigh(loc=0.0, scale=1.0),
stats.rice(b=0.775, loc=0.0, scale=1.0), stats.recipinvgauss(mu=0.63, loc=0.0, scale=1.0),
stats.semicircular(loc=0.0, scale=1.0), stats.t(df=2.74, loc=0.0, scale=1.0),
stats.triang(c=0.158, loc=0.0, scale=1.0), stats.truncexpon(b=4.69, loc=0.0, scale=1.0),
stats.truncnorm(a=0.1, b=2, loc=0.0, scale=1.0), stats.tukeylambda(lam=3.13, loc=0.0, scale=1.0),
stats.uniform(loc=0.0, scale=1.0), stats.vonmises(kappa=3.99, loc=0.0, scale=1.0),
stats.vonmises_line(kappa=3.99, loc=0.0, scale=1.0), stats.wald(loc=0.0, scale=1.0),
stats.weibull_min(c=1.79, loc=0.0, scale=1.0), stats.weibull_max(c=2.87, loc=0.0, scale=1.0),
stats.wrapcauchy(c=0.0311, loc=0.0, scale=1.0)
]
bins = 32
size = 16384
plotData = []
for distribution in DISTRIBUTIONS:
try:
# Create random data
rv = pd.Series(distribution.rvs(size=size))
# Get sane start and end points of distribution
start = distribution.ppf(0.01)
end = distribution.ppf(0.99)
# Build PDF and turn into pandas Series
x = np.linspace(start, end, size)
y = distribution.pdf(x)
pdf = pd.Series(y, x)
# Get histogram of random data
b = np.linspace(start, end, bins+1)
y, x = np.histogram(rv, bins=b, normed=True)
x = [(a+x[i+1])/2.0 for i,a in enumerate(x[0:-1])]
hist = pd.Series(y, x)
# Create distribution name and parameter string
title = '{}({})'.format(distribution.dist.name, ', '.join(['{}={:0.2f}'.format(k,v) for k,v in distribution.kwds.items()]))
# Store data for later
plotData.append({
'pdf': pdf,
'hist': hist,
'title': title
})
except Exception:
print 'could not create data', distribution.dist.name
plotMax = len(plotData)
for i, data in enumerate(plotData):
w = abs(abs(data['hist'].index[0]) - abs(data['hist'].index[1]))
# Display
plt.figure(figsize=(10, 6))
ax = data['pdf'].plot(kind='line', label='Model PDF', legend=True, lw=2)
ax.bar(data['hist'].index, data['hist'].values, label='Random Sample', width=w, align='center', alpha=0.5)
ax.set_title(data['title'])
# Grab figure
fig = matplotlib.pyplot.gcf()
# Output 'file'
fig.savefig('~/Desktop/dist/'+data['title']+'.png', format='png', bbox_inches='tight')
matplotlib.pyplot.close()