Is there any Python function/code to plot Binomial distribution (both PDF and CDF)

Question

All the code in the net do not let us decide both the parameters of binomial distribution.
How we can use a user interface (CLI) to ask user to enter any parameter (number of trials, probability of success), then plot the graphs in a suitable way?

Asked By: Oladiano Meriko Onaiker

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Source

Answer 1

Binomial distribution (PDF) is defined as : p(x;n) = nCr(n,x) * (p**x) * ((1-p)**(n-x))

The CDF can be easily generated by sending the PDF through a accumulator system (a summer). For that simply sum the PDF; up to and including the interested point.

How ever plotting the PDF and CDF can be nicely done if you can use stem function for low number of "n" (= number of trials) and plot function for larger values of "n".

Use these links if you do not know matplotlib.pyplot stem, plot functions:
1.
Python matplotlib.pyplot stem function
2.
Python matplotlib.pyplot plot function

import numpy as np
import matplotlib.pyplot as plt
import math
import time
def nCr(n,r):n=int(n);r=int(r);f = math.factorial;return int(f(n)/(f(r)*f(n-r)))
def p(n,p,x):return nCr(n,x) * (p**x) * ((1-p)**(n-x))
def cumilate(n,pS,x_):
    o=0
    for i in range(x_+1):
        o += p(n,pS,i)
    return o;
while True:
    input_n = input('Enter No. of trials:')
    input_pS = input('Enter Probability of success:')

    try:
        n = int(input_n)
        pS = float(input_pS)
    except :
        print('Please enter valid data...')
        continue

    if(n<=0):print('n should be larger than 0');continue
    if(not(0<=pS<=1)):print('p should be in [0,1]');continue
    if(n>11500):print('n is too large.It will stuck your pc.Try less than 500');continue
    x =  [i for i in range(n+1)]
    y = [p(n,pS,x1) for x1 in x]

    fig,ax = plt.subplots(2,1,figsize=(20,10))
    if(n>=150):
        ax[0].plot(x,y)
    else:
        ax[0].stem(x,y)
    ax[0].title.set_text('Binomial PDF n=' + str(n) +' pS=' + str(pS))

    cum = [cumilate(n,pS,x1) for x1 in x]
    if(n>=150):
        ax[1].plot(x,cum)
    else:
        ax[1].stem(x,cum)
    ax[1].title.set_text('Binomial CDF n=' + str(n) +' pS=' + str(pS))
    plt.show()
    print('-------------------- Plotted -----------------')

Results will look like following:
n = 120 , p = 0.5

n = 10, p =0.8

When the number of trials are so high, stem function is not visually nice to use. So switched to plot function and shown as a continuous function.
n = 200, p = 0.3

Answered By: R3KI3G

Is there any Python function/code to plot Binomial distribution (both PDF and CDF)

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