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 inlineimport ioimport numpy as npimport pandas as pdimport scipy.stats as statsimport matplotlibimport matplotlib.pyplot as pltmatplotlib.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 = 32size = 16384plotData = []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()

Visualizing all scipy probability distributions in a single figure

Here is a solution that displays all the scipy probability distributions in a single figure and avoids the need to copy-paste (or web scrape) the distribution shape parameters by extracting them instead from the _distr_params file that contains sane parameters for all the available distributions.

Similarly to the accepted answer, a sample of random variates is generated for each distribution. These samples are then stored in a pandas dataframe where the columns containing identical distribution names are renamed (based on 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 function which creates a grid of histograms. These plots are then overlaid with a line plot representing the probability density function ranging from the 0.1% quantile up to the 99.9% quantile.

There are a few additional things to point out:

• The location and scale parameters are set at the default values (0 and 1) for all the distributions.
• Some histograms show only a few very wide bars because of one or more outliers that are located outside of the 0.1-99.9% quantile limits.
• The plot width is limited to only 10 inches in this example so as to preserve the sharpness of the uploaded image. Because of this, you may notice that a few of the x labels (used as subtitles) overlap.
• There is no need to import matplotlib.pyplot seeing as the matplotlib objects are generated with the pandas plotting functions (unless you need plt.show).

The code for generating the x labels and the random variables is based on the accepted answer by tmthydvnprt and this answer by Adam Erickson in addition to the scipy documentation.

import numpy as np         # v 1.19.2from scipy import stats    # v 1.5.2import pandas as pd        # v 1.1.3pd.options.display.max_columns = 6np.random.seed(123)

size = 10000names, 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 labelsfor 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 samplesdf = 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 enddf.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 dimensionsnplot = df.columns.sizecols = 3rows = int(np.ceil(nplot/cols))subp_w = 10/cols  # 10 corresponds to the figure width in inchessubp_h = 0.9*subp_w# Create pandas grid of histogramsaxs = 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 formattingfor 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)

Related would be all distributions in MicceriRD!