Verification CLT via flask && matplotlib

 Central limit theorems (CLT) are a class of theorems in probability theory stating that the sum of a sufficiently large number of weakly dependent random variables that have approximately the same scale (none of the terms dominates, does not make a decisive contribution to the sum), has a distribution close to normal. Since many random variables in applications are formed under the influence of several weakly dependent random factors, their distribution is considered normal. In this case, the condition must be observed that none of the factors is dominant. Central limit theorems in these cases justify the application of the normal distribution.

Following below is python code to be run by flask framework

(.env) boris@boris-All-Series:~/flaskmatplotlib$ cat  flaskMatplotlib7.py

import io

from flask import Response

from matplotlib.backends.backend_agg import FigureCanvasAgg as FigureCanvas

from matplotlib.figure import Figure

from flask import Flask

import matplotlib.pyplot as plt

import numpy as np

import scipy.stats as stats

plt.rcParams["figure.figsize"] = [14.50, 10.50]

plt.rcParams["figure.autolayout"] = True

app = Flask(__name__)

@app.route('/print-plot')

def plot_png():

   fig = Figure()

   axes = fig.add_subplot(1, 1, 1)

   axes.set_title('CLT via flask&&matplotlib, Refresh Screen a couple of times',fontsize = 15, color = 'black')

   n = 10000

   avg = []

   for i in range(1,n):

       a = np.random.randint(1,7,10)

       avg.append(np.average(a))

   # Normalise this histogram too

   axes.hist(avg[0:], 20, density=True, stacked=True)

   avg1 = []

   for i in range(1,n):

       a = np.random.randint(1,7,10)

       avg1.append(np.average(a))

   # Normalise this histogram too

   axes.hist(avg1[0:], 20, density=True, stacked=True)

   avg2 = []

   for i in range(1,n):

       a = np.random.randint(1,7,10)

       avg2.append(np.average(a))

   # Normalise this histogram too

   axes.hist(avg2[0:], 20, density=True, stacked=True)

   avg3 = []

   for i in range(1,n):

       a = np.random.randint(1,7,10)

       avg3.append(np.average(a))

   # Normalise this histogram too

   axes.hist(avg3[0:], 20, density=True, stacked=True)

   zscore = stats.zscore((avg[0:]+avg1[0:]+avg2[0:]+avg3[0:]))

   mu, sigma = np.mean(avg+avg1+avg2+avg3), np.std(avg+avg1+avg2+avg3)

   s = np.random.normal(mu, sigma, 10000)

   # Create the bins and histogram

   count, bins, ignored = axes.hist(s, 20, density=True, stacked=True) 

   # Use scipy.stats implementation of the normal pdf

   # Plot the distribution curve

   x = np.linspace(1.5, 5.5, num=100)

   axes.plot(x, stats.norm.pdf(x, mu, sigma))

   output = io.BytesIO()

   FigureCanvas(fig).print_png(output)

   return Response(output.getvalue(), mimetype='image/png')

$  export FLASK_ENV=development

$  export FLASK_DEBUG=1

$  export FLASK_APP=flaskMatplotlib7.py

(.env) boris@boris-All-Series:~/flaskmatplotlib$ flask run

WARNING: This is a development server. Do not use it in a production deployment. Use a production WSGI server instead.

 * Serving Flask app 'flaskMatplotlib7.py'

 * Debug mode: on

 * Running on http://127.0.0.1:5000 (Press CTRL+C to quit)

 * Restarting with stat

 * Debugger is active!

 * Debugger PIN: 452-793-879

Another version of python code. Just looping when creating histograms.

(.env) boris@boris-All-Series:~/flaskmatplotlib$ cat flaskMatplotlib10.py

import io

from flask import Response

from matplotlib.backends.backend_agg import FigureCanvasAgg as FigureCanvas

from matplotlib.figure import Figure

from flask import Flask

import matplotlib.pyplot as plt

import numpy as np

import scipy.stats as stats

import warnings

warnings.filterwarnings('ignore')

plt.rcParams["figure.figsize"] = [15.50, 11.50]

plt.rcParams["figure.autolayout"] = True

app = Flask(__name__)

@app.route('/print-plot')

def plot_png():

   fig = Figure()

   axes = fig.add_subplot(1, 1, 1)

   axes.set_title('Verification CLT via flask&&matplotlib, Refresh Screen a couple of times',fontsize = 15, color = 'black')

   n = 10000

   longlst = []

   sigmalst = []

   lst = ["avg","avg1","avg2","avg3"]

   for avs in lst:

       avs = [] 

       for i in range(1,n):

         a = np.random.randint(1,7,10)

         avs.append(np.average(a))

       # Normalise this histogram too

       axes.hist(avs[0:], 20, density=True, stacked=True)

       longlst = longlst + avs[0:]

       sigmalst = sigmalst + avs[:]

   zscore = stats.zscore(longlst)

   mu, sigma = np.mean(sigmalst), np.std(sigmalst)

   s = np.random.normal(mu, sigma, 10000)

   # Create the bins and histogram

   count, bins, ignored = axes.hist(s, 20, density=True, stacked=True) 

   # Use scipy.stats implementation of the normal pdf

   # Plot the distribution curve

   x = np.linspace(1.5, 6.5, num=100)

   axes.plot(x, stats.norm.pdf(x, mu, sigma))

   output = io.BytesIO()

   FigureCanvas(fig).print_png(output)

   return Response(output.getvalue(), mimetype='image/png')

(.env) boris@boris-All-Series:~/flaskmatplotlib$ flask run

WARNING: This is a development server. Do not use it in a production deployment. Use a production WSGI server instead.

 * Serving Flask app 'flaskMatplotlib10.py'

 * Debug mode: on

 * Running on http://127.0.0.1:5000 (Press CTRL+C to quit)

 * Restarting with stat

 * Debugger is active!

 * Debugger PIN: 255-673-976