scipy.stats 中可用的所有发行版是什么样的？
What do all the distributions available in scipy.stats look like?
可视化 scipy.stats 分布
可以制作直方图 the scipy.stats normal random variable 以查看分布情况。
% 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)
其他分布是什么样的？
可视化所有 scipy.stats distributions
基于 list of scipy.stats distributions, plotted below are the histograms and PDFs of each continuous random variable. The code used to generate each distribution is 。注意：形状常数取自 scipy.stats 分布文档页面上的示例。
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)
生成代码
这里是用来生成绘图的 Jupyter Notebook。
%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()
在一张图中可视化所有 scipy 概率分布
这是一个解决方案，它在单个图中显示所有 scipy 概率分布，并通过从 _distr_params 包含所有可用发行版的合理参数的文件。
与接受的答案类似，为每个分布生成随机变量样本。然后将这些样本存储在 pandas 数据框中，其中包含相同分布名称的列被重命名（基于创建直方图网格的 this answer by MaxU) because some distributions are listed more than once with different parameter definitions (e.g. kappa4). This way, the samples can be plotted using the convenient df.hist 函数。然后将这些图与表示概率的线图叠加密度函数范围从 0.1% 分位数到 99.9% 分位数。
还有几点需要指出：
- 所有分布的位置和比例参数都设置为默认值（0 和 1）。
- 一些直方图仅显示几个非常宽的条形，因为一个或多个异常值位于 0.1-99.9% 分位数限制之外。
- 本例中绘图宽度限制为仅 10 英寸，以保持上传图像的清晰度。因此，您可能会注意到一些 x 标签（用作字幕）重叠。
- 无需导入
matplotlib.pyplot，因为 matplotlib 对象是使用 pandas 绘图函数生成的（除非您需要 plt.show）。
生成 x 标签和随机变量的代码基于 tmthydvnprt 接受的答案和 in addition to the scipy documentation。
import numpy as np # v 1.19.2
from scipy import stats # v 1.5.2
import pandas as pd # v 1.1.3
pd.options.display.max_columns = 6
np.random.seed(123)
size = 10000
names, xlabels, frozen_rvs, samples = [], [], [], []
# Extract names and sane parameters of all scipy probability distributions
# (except the deprecated ones) and loop through them to create lists of names,
# frozen random variables, samples of random variates and x labels
for name, params in stats._distr_params.distcont:
if name not in ['frechet_l', 'frechet_r']:
loc, scale = 0, 1
names.append(name)
params = list(params) + [loc, scale]
# Create instance of random variable
dist = getattr(stats, name)
# Create frozen random variable using parameters and add it to the list
# to be used to draw the probability density functions
rv = dist(*params)
frozen_rvs.append(rv)
# Create sample of random variates
samples.append(rv.rvs(size=size))
# Create x label containing the distribution parameters
p_names = ['loc', 'scale']
if dist.shapes:
p_names = [sh.strip() for sh in dist.shapes.split(',')] + ['loc', 'scale']
xlabels.append(', '.join([f'{pn}={pv:.2f}' for pn, pv in zip(p_names, params)]))
# Create pandas dataframe containing all the samples
df = pd.DataFrame(data=np.array(samples).T, columns=[name for name in names])
# Rename the duplicate column names by adding a period and an integer at the end
df.columns = pd.io.parsers.ParserBase({'names':df.columns})._maybe_dedup_names(df.columns)
df.head()
# alpha anglit arcsine ... weibull_max weibull_min wrapcauchy
# 0 0.327165 0.166185 0.018339 ... -0.928914 0.359808 4.454122
# 1 0.241819 0.373590 0.630670 ... -0.733157 0.479574 2.778336
# 2 0.231489 0.352024 0.457251 ... -0.580317 1.312468 4.932825
# 3 0.290551 -0.133986 0.797215 ... -0.954856 0.341515 3.874536
# 4 0.334494 -0.353015 0.439837 ... -1.440794 0.498514 5.195171
# Set parameters for figure dimensions
nplot = df.columns.size
cols = 3
rows = int(np.ceil(nplot/cols))
subp_w = 10/cols # 10 corresponds to the figure width in inches
subp_h = 0.9*subp_w
# Create pandas grid of histograms
axs = df.hist(density=True, bins=15, grid=False, edgecolor='w',
linewidth=0.5, legend=False,
layout=(rows, cols), figsize=(cols*subp_w, rows*subp_h))
# Loop over subplots to draw probability density function and apply some
# additional formatting
for idx, ax in enumerate(axs.flat[:df.columns.size]):
rv = frozen_rvs[idx]
x = np.linspace(rv.ppf(0.001), rv.ppf(0.999), size)
ax.plot(x, rv.pdf(x), c='black', alpha=0.5)
ax.set_title(ax.get_title(), pad=25)
ax.set_xlim(x.min(), x.max())
ax.set_xlabel(xlabels[idx], fontsize=8, labelpad=10)
ax.xaxis.set_label_position('top')
ax.tick_params(axis='both', labelsize=9)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.figure.subplots_adjust(hspace=0.8, wspace=0.3)
可视化 scipy.stats 分布
可以制作直方图 the scipy.stats normal random variable 以查看分布情况。
% 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)
其他分布是什么样的？
可视化所有 scipy.stats distributions
基于 list of scipy.stats distributions, plotted below are the histograms and PDFs of each continuous random variable. The code used to generate each distribution is
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)
生成代码
这里是用来生成绘图的 Jupyter Notebook。
%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()
在一张图中可视化所有 scipy 概率分布
这是一个解决方案，它在单个图中显示所有 scipy 概率分布，并通过从 _distr_params 包含所有可用发行版的合理参数的文件。
与接受的答案类似，为每个分布生成随机变量样本。然后将这些样本存储在 pandas 数据框中，其中包含相同分布名称的列被重命名（基于创建直方图网格的 this answer by MaxU) because some distributions are listed more than once with different parameter definitions (e.g. kappa4). This way, the samples can be plotted using the convenient df.hist 函数。然后将这些图与表示概率的线图叠加密度函数范围从 0.1% 分位数到 99.9% 分位数。
还有几点需要指出：
- 所有分布的位置和比例参数都设置为默认值（0 和 1）。
- 一些直方图仅显示几个非常宽的条形，因为一个或多个异常值位于 0.1-99.9% 分位数限制之外。
- 本例中绘图宽度限制为仅 10 英寸，以保持上传图像的清晰度。因此，您可能会注意到一些 x 标签（用作字幕）重叠。
- 无需导入
matplotlib.pyplot，因为 matplotlib 对象是使用 pandas 绘图函数生成的（除非您需要plt.show）。
生成 x 标签和随机变量的代码基于 tmthydvnprt 接受的答案和
import numpy as np # v 1.19.2
from scipy import stats # v 1.5.2
import pandas as pd # v 1.1.3
pd.options.display.max_columns = 6
np.random.seed(123)
size = 10000
names, xlabels, frozen_rvs, samples = [], [], [], []
# Extract names and sane parameters of all scipy probability distributions
# (except the deprecated ones) and loop through them to create lists of names,
# frozen random variables, samples of random variates and x labels
for name, params in stats._distr_params.distcont:
if name not in ['frechet_l', 'frechet_r']:
loc, scale = 0, 1
names.append(name)
params = list(params) + [loc, scale]
# Create instance of random variable
dist = getattr(stats, name)
# Create frozen random variable using parameters and add it to the list
# to be used to draw the probability density functions
rv = dist(*params)
frozen_rvs.append(rv)
# Create sample of random variates
samples.append(rv.rvs(size=size))
# Create x label containing the distribution parameters
p_names = ['loc', 'scale']
if dist.shapes:
p_names = [sh.strip() for sh in dist.shapes.split(',')] + ['loc', 'scale']
xlabels.append(', '.join([f'{pn}={pv:.2f}' for pn, pv in zip(p_names, params)]))
# Create pandas dataframe containing all the samples
df = pd.DataFrame(data=np.array(samples).T, columns=[name for name in names])
# Rename the duplicate column names by adding a period and an integer at the end
df.columns = pd.io.parsers.ParserBase({'names':df.columns})._maybe_dedup_names(df.columns)
df.head()
# alpha anglit arcsine ... weibull_max weibull_min wrapcauchy
# 0 0.327165 0.166185 0.018339 ... -0.928914 0.359808 4.454122
# 1 0.241819 0.373590 0.630670 ... -0.733157 0.479574 2.778336
# 2 0.231489 0.352024 0.457251 ... -0.580317 1.312468 4.932825
# 3 0.290551 -0.133986 0.797215 ... -0.954856 0.341515 3.874536
# 4 0.334494 -0.353015 0.439837 ... -1.440794 0.498514 5.195171
# Set parameters for figure dimensions
nplot = df.columns.size
cols = 3
rows = int(np.ceil(nplot/cols))
subp_w = 10/cols # 10 corresponds to the figure width in inches
subp_h = 0.9*subp_w
# Create pandas grid of histograms
axs = df.hist(density=True, bins=15, grid=False, edgecolor='w',
linewidth=0.5, legend=False,
layout=(rows, cols), figsize=(cols*subp_w, rows*subp_h))
# Loop over subplots to draw probability density function and apply some
# additional formatting
for idx, ax in enumerate(axs.flat[:df.columns.size]):
rv = frozen_rvs[idx]
x = np.linspace(rv.ppf(0.001), rv.ppf(0.999), size)
ax.plot(x, rv.pdf(x), c='black', alpha=0.5)
ax.set_title(ax.get_title(), pad=25)
ax.set_xlim(x.min(), x.max())
ax.set_xlabel(xlabels[idx], fontsize=8, labelpad=10)
ax.xaxis.set_label_position('top')
ax.tick_params(axis='both', labelsize=9)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.figure.subplots_adjust(hspace=0.8, wspace=0.3)