scipy.stats 中可用的所有分布是什么样的? [英] What do all the distributions available in scipy.stats look like?

问题描述

可视化

其他分布是什么样的?

解决方案

Visualizing all

生成代码

这是用于生成绘图的 Jupyter Notebook.

%matplotlib 内联导入 io将 numpy 导入为 np将熊猫导入为 pd导入 scipy.stats 作为统计信息导入 matplotlib导入 matplotlib.pyplot 作为 pltmatplotlib.rcParams['figure.figsize'] = (16.0, 14.0)matplotlib.style.use('ggplot')

<小时>

# 要检查的分布，形状常量取自 scipy.stats 分布文档页面上的示例.分布 = [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)]

<小时>

bins = 32size = 16384plotData = []for distribution in DISTRIBUTIONS:尝试:# Create random datarv = pd.Series(distribution.rvs(size=size))# Get sane start and end points of distributionstart = distribution.ppf(0.01)end = distribution.ppf(0.99)# Build PDF and turn into pandas Seriesx = np.linspace(start, end, size)y = distribution.pdf(x)pdf = pd.Series(y, x)# Get histogram of random datab = 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 stringtitle = '{}({})'.format(distribution.dist.name, ', '.join(['{}={:0.2f}'.format(k,v) for k,v in distribution.kwds.items()]))# Store data for laterplotData.append({'pdf': pdf,'hist': hist,'title': title})except Exception:print 'could not create data', distribution.dist.name

<小时>

plotMax = len(plotData)for i, data in enumerate(plotData):w = abs(abs(data['hist'].index[0]) - abs(data['hist'].index[1]))# Displayplt.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 figurefig = matplotlib.pyplot.gcf()# Output 'file'fig.savefig('~/Desktop/dist/'+data['title']+'.png', format='png', bbox_inches='tight')matplotlib.pyplot.close()

Visualizing scipy.stats distributions

A histogram can be made of the scipy.stats normal random variable to see what the distribution looks like.

% 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)

What do the other distributions look like?

解决方案

Visualizing all scipy.stats distributions

Based on the 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 at the bottom. Note: The shape constants were taken from the examples on the scipy.stats distribution documentation pages.

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)

Generation Code

Here is the Jupyter Notebook used to generate the plots.

%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()

这篇关于scipy.stats 中可用的所有分布是什么样的?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！