Develop Reference

Integrating a histogram in a bootstrap simulation graph

I have a dataframe with 1000 simulations of a portfolio's returns. I am able to graph the simulations and do the respective histogram separately, but I have absolutely no idea how to merge them in order to resemble the following image:
please take this example of data in order to facilitate answers:
import numpy as np
import pandas as pd
def simulate_panel(T, N):
"""" This function simulates return paths"""
dates = pd.date_range("20210218", periods=T, freq='D')
columns = []
for i in range(N):
columns.append(str(i+1))
return pd.DataFrame(np.random.normal(0, 0.01, size=(T, N)), index=dates,
columns=columns)
df=(1+simulate_panel(1000,1000)).cumprod()
df.plot(figsize=(8,6),title=('Bootstrap'), legend=False)
Thank you very much in advance.

To color the curves via their last value, they can be drawn one-by-one. With a colormap and a norm, the value can be converted to the appropriate color. Using some transparency (alpha), the most visited positions will be colored stronger.
In a second subplot, a vertical histogram can be drawn, with the bars colored similarly.
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
def simulate_panel(T, N):
"""" This function simulates return paths"""
dates = pd.date_range("20210218", periods=T, freq='D')
columns = [(str(i + 1)) for i in range(N)]
return pd.DataFrame(np.random.normal(0, 0.01, size=(T, N)), index=dates, columns=columns)
df = (1 + simulate_panel(1000, 1000)).cumprod()
fig, (ax1, ax2) = plt.subplots(ncols=2, sharey=True, figsize=(12, 4),
gridspec_kw={'width_ratios': [5, 1], 'wspace': 0})
data = df.to_numpy().T
cmap = plt.cm.get_cmap('turbo')
norm = plt.Normalize(min(data[:, -1]), max(data[:, -1]))
for row in data:
ax1.plot(df.index, row, c=cmap(norm(row[-1])), alpha=0.1)
ax1.margins(x=0)
_, bin_edges, bars = ax2.hist(data[:, -1], bins=20, orientation='horizontal')
for x0, x1, bar in zip(bin_edges[:-1], bin_edges[1:], bars):
bar.set_color(cmap(norm((x0 + x1) / 2)))
ax2.tick_params(left=False)
plt.tight_layout()
plt.show()

You can use GridSpec to set up axes for line chart and the histogram next to each other:
import matplotlib.pyplot as plt
import matplotlib.cm as cm
# layout
fig = plt.figure()
gs = fig.add_gridspec(1, 2, wspace=0, width_ratios=[9, 1])
ax = gs.subplots(sharey=True)
# line chart
z = df.iloc[-1]
df.plot(figsize=(8,6), title=('Bootstrap'), legend=False, ax=ax[0],
color=cm.RdYlBu_r((z - z.min()) / (z.max() - z.min())))
# histogram
n_bins = 20
cnt, bins, patches = ax[1].hist(
z, np.linspace(z.min(), z.max(), n_bins),
ec='k', orientation='horizontal')
colors = cm.RdYlBu_r((bins - z.min()) / (z.max() - z.min()))
for i, p in enumerate(patches):
p.set_color(colors[i])

Matplotlib fill_between edge

I need to create a plot as close to this picture as possible (given the generated dataframe code below):
And here's the output plot of my code:
What I am having problems with is:
The edge of fill_between is not sharp as in the picture. What I have is some kind of white shadow. How do I change the line between the fillings to match a target picture?
How do I aling legend color lines to the center, but not to the left border which my code does?
Here's my code:
import matplotlib.pyplot as plt
import matplotlib.colors as colors
import matplotlib.cm as cm
import numpy as np
import pandas as pd
ncols = 10
figsize = (20, 5)
fontsize = 14
dti = pd.date_range('2013-01-01', '2020-12-31', freq='2W')
probabilities_in_time = np.random.random((ncols, len(dti)))
probabilities_in_time = probabilities_in_time / \
probabilities_in_time.sum(axis=0)
probabilities_in_time = pd.DataFrame(probabilities_in_time).T
probabilities_in_time.index = dti
cm_subsection = np.linspace(0, 1, ncols)
colors = [cm.coolwarm(x) for x in cm_subsection]
def plot_time_probabilities(probabilities_in_time, figsize):
plt.figure(figsize=figsize)
plt.yticks(np.arange(0, 1.2, 0.2), fontsize=fontsize)
plt.xticks(fontsize=fontsize)
draw_stack_plot(colors, probabilities_in_time)
set_grid()
set_legend()
plt.show()
def draw_stack_plot(colors, probabilities_in_time):
for i, color in enumerate(colors):
if i == 0:
plt.plot(probabilities_in_time[i], color=color)
plt.fill_between(probabilities_in_time.index,
probabilities_in_time[0], color=color)
else:
probabilities_in_time[i] += probabilities_in_time[i-1]
plt.fill_between(probabilities_in_time.index,
probabilities_in_time[i], probabilities_in_time[i-1],
color=color)
plt.plot(probabilities_in_time[i], label=' Probability: {}'.format(
i), color=color)
def set_grid():
ax = plt.gca()
ax.set_axisbelow(False)
ax.xaxis.grid(True, linestyle='-', lw=1)
def set_legend():
leg = plt.legend(loc='lower left', fontsize=14, handlelength=1.3)
for i in leg.legendHandles:
i.set_linewidth(12)
plot_time_probabilities(probabilities_in_time, figsize)

To set the legend in the center, you can set loc='center', or you can put the legend outside. To avoid that the legend handles grow to larger, you can leave out .set_linewidth(12) (this sets a very wide edge width of 12 points).
Shifting the colors by one position can help to show the fill borders more pronounced. To still have a correct legend, the label should then be added to fill_between.
The code below also tries to simplify part of the calls:
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import numpy as np
import pandas as pd
ncols = 10
figsize = (20, 5)
fontsize = 14
dti = pd.date_range('2013-01-01', '2020-12-31', freq='2W')
probabilities_in_time = np.random.random((ncols, len(dti)))
probabilities_in_time = probabilities_in_time / probabilities_in_time.sum(axis=0)
probabilities_in_time = pd.DataFrame(probabilities_in_time).T
probabilities_in_time.index = dti
cm_subsection = np.linspace(0, 1, ncols)
colors = cm.coolwarm(cm_subsection)
def plot_time_probabilities(probabilities_in_time, figsize):
plt.figure(figsize=figsize)
plt.yticks(np.arange(0, 1.2, 0.2), fontsize=fontsize)
plt.xticks(fontsize=fontsize)
draw_stack_plot(colors, probabilities_in_time)
set_grid()
set_legend()
# plt.margins(x=0, y=0)
plt.margins(x=0.02)
plt.tight_layout()
plt.show()
def draw_stack_plot(colors, probabilities_in_time):
current_probabilities = 0
for i, color in enumerate(colors):
plt.fill_between(probabilities_in_time.index,
probabilities_in_time[i] + current_probabilities, current_probabilities,
color=color, label=f' Probability: {i}')
current_probabilities += probabilities_in_time[i]
plt.plot(current_probabilities,
color=colors[0] if i <= 1 else colors[-1] if i >= 8 else colors[i - 1] if i < 5 else colors[i + 1])
def set_grid():
ax = plt.gca()
ax.set_axisbelow(False)
ax.xaxis.grid(True, linestyle='-', lw=1)
def set_legend():
leg = plt.legend(loc='lower left', fontsize=14, handlelength=1.3)
# leg = plt.legend(loc='upper left', bbox_to_anchor=(1.01, 1), fontsize=14, handlelength=1.3)
# for i in leg.legendHandles:
# i.set_linewidth(12)
plot_time_probabilities(probabilities_in_time, figsize)

Frequency Distribution Plot: change x-axis to interval

Dear People of the Internet
I have calculated a frequency distribution and I would now like to plot it in a certain manner. So far I have calculated and plotted the frequency distribution, but I couldn't find a solution for the endproduct I am looking for. My code with an example dataset for now is:
import matplotlib.pyplot as plt
from scipy import stats
import numpy as np
import pandas as pd
# example data
rng = np.random.RandomState(seed=12345)
a1 = stats.norm.rvs(size=1000, random_state=rng)
res = stats.relfreq(a1, numbins=34)
x = res.lowerlimit + np.linspace(0, res.binsize*res.frequency.size, res.frequency.size)
# plotting
fig = plt.figure(figsize=(6, 3))
ax = fig.add_subplot(1, 1, 1)
ax.bar(x, res.frequency, width=res.binsize)
ax.set_title('Frequency Distribution of 1D Vix Returns')
ax.set_xlim([x.min(), x.max()])
ax.set_xticks(ax.get_xticks()[::1])
plt.show()
As a last step, I would like to plot the x-Axis just as in the attached picture. Instead of single number I would like to have the interval. I couldn't find a source in which this matter is resolved. Has anyone encountered the same problem or knows any source which has a solution to it? Thanks in advance

Have a look at this nice answer:
https://stackoverflow.com/a/6353051/10372616.
I added the code to your current plot.
import matplotlib.pyplot as plt
from scipy import stats # ????
import numpy as np
import pandas as pd # ????
# example data
rng = np.random.RandomState(seed=12345)
a1 = stats.norm.rvs(size=1000, random_state=rng)
res = stats.relfreq(a1, numbins=34)
x = res.lowerlimit + np.linspace(0, res.binsize*res.frequency.size, res.frequency.size)
# plotting
fig = plt.figure(figsize=(6, 3))
ax = fig.add_subplot(1, 1, 1)
ax.bar(x, res.frequency, width=res.binsize)
ax.set_title('Frequency Distribution of 1D Vix Returns')
ax.set_xlim([x.min(), x.max()])
ax.set_xticks(ax.get_xticks()[::1])
# Change traditional tick labels to range labels
# ----------------------------------------------------------------
ax.set_xticklabels([]) # hide your previous x tick labels
bins = ax.get_xticks()[::1]
bin_centers = 0.5 * np.diff(bins) + bins[:-1]
for a, b, x in zip(bins, bins[1:], bin_centers):
label = '{:0.0f} to {:0.0f}'.format(a, b)
ax.annotate(label, xy=(x, 0), xycoords=('data', 'axes fraction'),
xytext=(0, -10), textcoords='offset points', va='top', ha='center', rotation=90)
plt.show()
Before:
After:

Plotting annotated gaussian curve

u am trying to recreate the image below. Most problematic is putting the percentages and labels on the plot.
So far I did manage to plot the gaussian, although be it a bit steep... Any idea how to get the exact percentages there?
from matplotlib import pyplot as mp
import numpy as np
def gaussian(x, mu, sig):
return np.exp(-np.power(x - mu, 2.) / (2 * np.power(sig, 2.)))
for mu, sig in [(0, 3)]:
mp.plot(gaussian(np.linspace(-10, 10, 120), mu, sig))
mp.show()
UPDATE:
What if I would use a trick approach such as the one below, but somehow hide the histogram blocks?
import numpy as np
import scipy
import pandas as pd
from scipy.stats import norm
import matplotlib.pyplot as plt
from matplotlib.mlab import normpdf
# dummy data
mu = 0
sigma = 1
n_bins = 50
s = np.random.normal(mu, sigma, 1000000)
fig, axes = plt.subplots(nrows=2, ncols=1, sharex=True)
#histogram
n, bins, patches = axes[1].hist(s, n_bins, normed=True, alpha=.1, edgecolor='black' )
pdf = 1/(sigma*np.sqrt(2*np.pi))*np.exp(-(bins-mu)**2/(2*sigma**2))
median, q1, q3 = np.percentile(s, 50), np.percentile(s, 25), np.percentile(s, 75)
print(q1, median, q3)
#probability density function
axes[1].plot(bins, pdf, color='orange', alpha=.6)
#to ensure pdf and bins line up to use fill_between.
bins_1 = bins[(bins >= q1-1.5*(q3-q1)) & (bins <= q1)] # to ensure fill starts from Q1-1.5*IQR
bins_2 = bins[(bins <= q3+1.5*(q3-q1)) & (bins >= q3)]
pdf_1 = pdf[:int(len(pdf)/2)]
pdf_2 = pdf[int(len(pdf)/2):]
pdf_1 = pdf_1[(pdf_1 >= norm(mu,sigma).pdf(q1-1.5*(q3-q1))) & (pdf_1 <= norm(mu,sigma).pdf(q1))]
pdf_2 = pdf_2[(pdf_2 >= norm(mu,sigma).pdf(q3+1.5*(q3-q1))) & (pdf_2 <= norm(mu,sigma).pdf(q3))]
#fill from Q1-1.5*IQR to Q1 and Q3 to Q3+1.5*IQR
axes[1].fill_between(bins_1, pdf_1, 0, alpha=.6, color='orange')
axes[1].fill_between(bins_2, pdf_2, 0, alpha=.6, color='orange')
print(norm(mu, sigma).cdf(median))
print(norm(mu, sigma).pdf(median))
#add text to bottom graph.
axes[1].annotate("{:.1f}%".format(100*norm(mu, sigma).cdf(q1)), xy=((q1-1.5*(q3-q1)+q1)/2, 0), ha='center')
axes[1].annotate("{:.1f}%".format(100*(norm(mu, sigma).cdf(q3)-norm(mu, sigma).cdf(q1))), xy=(median, 0), ha='center')
axes[1].annotate("{:.1f}%".format(100*(norm(mu, sigma).cdf(q3+1.5*(q3-q1)-q3)-norm(mu, sigma).cdf(q3))), xy=((q3+1.5*(q3-q1)+q3)/2, 0), ha='center')
axes[1].annotate('q1', xy=(q1, norm(mu, sigma).pdf(q1)), ha='center')
axes[1].annotate('q3', xy=(q3, norm(mu, sigma).pdf(q3)), ha='center')
axes[1].set_ylabel('probability')
#top boxplot
axes[0].boxplot(s, 0, 'gD', vert=False)
axes[0].axvline(median, color='orange', alpha=.6, linewidth=.5)
axes[0].axis('off')
plt.subplots_adjust(hspace=0)
plt.show()

How to plot normal distribution with percentage of data as label in each band/bin?

While plotting normal distribution graph of data, how can we put labels like in image below for percentage of data in each bin where each band has a width of 1 standard deviation using matplotlib/seaborn or plotly ?
Currently, im plotting like this:
hmean = np.mean(data)
hstd = np.std(data)
pdf = stats.norm.pdf(data, hmean, hstd)
plt.plot(data, pdf)

Although I've labelled the percentages between the quartiles, this bit of code may be helpful to do the same for the standard deviations.
import numpy as np
import scipy
import pandas as pd
from scipy.stats import norm
import matplotlib.pyplot as plt
from matplotlib.mlab import normpdf
# dummy data
mu = 0
sigma = 1
n_bins = 50
s = np.random.normal(mu, sigma, 1000)
fig, axes = plt.subplots(nrows=2, ncols=1, sharex=True)
#histogram
n, bins, patches = axes[1].hist(s, n_bins, normed=True, alpha=.1, edgecolor='black' )
pdf = 1/(sigma*np.sqrt(2*np.pi))*np.exp(-(bins-mu)**2/(2*sigma**2))
median, q1, q3 = np.percentile(s, 50), np.percentile(s, 25), np.percentile(s, 75)
print(q1, median, q3)
#probability density function
axes[1].plot(bins, pdf, color='orange', alpha=.6)
#to ensure pdf and bins line up to use fill_between.
bins_1 = bins[(bins >= q1-1.5*(q3-q1)) & (bins <= q1)] # to ensure fill starts from Q1-1.5*IQR
bins_2 = bins[(bins <= q3+1.5*(q3-q1)) & (bins >= q3)]
pdf_1 = pdf[:int(len(pdf)/2)]
pdf_2 = pdf[int(len(pdf)/2):]
pdf_1 = pdf_1[(pdf_1 >= norm(mu,sigma).pdf(q1-1.5*(q3-q1))) & (pdf_1 <= norm(mu,sigma).pdf(q1))]
pdf_2 = pdf_2[(pdf_2 >= norm(mu,sigma).pdf(q3+1.5*(q3-q1))) & (pdf_2 <= norm(mu,sigma).pdf(q3))]
#fill from Q1-1.5*IQR to Q1 and Q3 to Q3+1.5*IQR
axes[1].fill_between(bins_1, pdf_1, 0, alpha=.6, color='orange')
axes[1].fill_between(bins_2, pdf_2, 0, alpha=.6, color='orange')
print(norm(mu, sigma).cdf(median))
print(norm(mu, sigma).pdf(median))
#add text to bottom graph.
axes[1].annotate("{:.1f}%".format(100*norm(mu, sigma).cdf(q1)), xy=((q1-1.5*(q3-q1)+q1)/2, 0), ha='center')
axes[1].annotate("{:.1f}%".format(100*(norm(mu, sigma).cdf(q3)-norm(mu, sigma).cdf(q1))), xy=(median, 0), ha='center')
axes[1].annotate("{:.1f}%".format(100*(norm(mu, sigma).cdf(q3+1.5*(q3-q1)-q3)-norm(mu, sigma).cdf(q3))), xy=((q3+1.5*(q3-q1)+q3)/2, 0), ha='center')
axes[1].annotate('q1', xy=(q1, norm(mu, sigma).pdf(q1)), ha='center')
axes[1].annotate('q3', xy=(q3, norm(mu, sigma).pdf(q3)), ha='center')
axes[1].set_ylabel('probability')
#top boxplot
axes[0].boxplot(s, 0, 'gD', vert=False)
axes[0].axvline(median, color='orange', alpha=.6, linewidth=.5)
axes[0].axis('off')
plt.subplots_adjust(hspace=0)
plt.show()

Since I unfortunately can't comment. Here is an alternative for #MaMo and #Chipmunk_da.
The problem is that the arrays 'bins_1, pdf_1' and 'bins_2, pdf_2' have different sizes. I solved it a bit rudimentary with the code lines written below, but it worked. Since now all arrays have the same size and map the variables of the Gaussian distribution.
The bounds are now no longer solved by the function of the comparison characters, as by #Chris, but with the definition of two variables 'bins_1, bins_2' and the NumPy function 'np.linspace'.
bins_1 = np.linspace(q1-1.5*(q3-q1), q1, n_bins, dtype=float)
pdf_1 = 1/(sigma*np.sqrt(2*np.pi))*np.exp(-(bins_1-mu)**2/(2*sigma**2))
bins_2 = np.linspace(q3+1.5*(q3-q1), q3, n_bins, dtype=float)
pdf_2 = 1/(sigma*np.sqrt(2*np.pi))*np.exp(-(bins_2-mu)**2/(2*sigma**2))