scipy.stats 分布可以用the scipy.stats normal random variable 制作直方图以查看分布情况。
% 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？
【问题讨论】：
标签： python matplotlib scipy statistics distribution
scipy.stats distributions
基于list of scipy.stats distributions，下面绘制的是每个continuous random variable 的histograms 和PDFs。用于生成每个分布的代码是at the bottom。注意：形状常量取自 scipy.stats 分发文档页面上的示例。
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)这是用于生成绘图的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()
【讨论】：
这是一个解决方案，它在单个图形中显示所有 scipy 概率分布，并通过从包含合理参数的 _distr_params 文件中提取分布形状参数来避免复制粘贴（或网络抓取）分布形状参数的需要所有可用的发行版。
与接受的答案类似，为每个分布生成一个随机变量样本。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this answer by MaxU），因为某些分布被多次列出，具有不同的参数定义（例如 kappa4）。这样，可以使用方便的df.hist 函数绘制样本，该函数创建直方图网格。然后将这些图与表示从 0.1% 分位数到 99.9% 分位数范围内的概率密度函数的线图重叠。
还有几点需要指出：
matplotlib.pyplot，因为 matplotlib 对象是使用 pandas 绘图功能生成的（除非您需要 plt.show）。生成 x 标签和随机变量的代码基于 tmthydvnprt 和 this answer by Adam Erickson 以及 the scipy documentation 接受的答案。
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)
【讨论】：
相关的是 MicceriRD 中的所有发行版！
【讨论】：