Try transcribing the probability mass function of the binomial distribution in Python

I'm interested in mathematics and statistics, but when I look at mathematical formulas, there are too many symbols to tell which one is which, or I forget it immediately, so I decided to write what I learned in the program. Did.

This time, we will create a class with the following functions for the binomial distribution with a total number of trials n times and a success probability p.

--Obtain the probability mass of the number of successes x --Get the lower cumulative probability of x --Get the upper cumulative probability of x --Draw a graph

Performance is not considered as it is intended to remember the contents of the expression.

The formula to reproduce in Python this time

When Bernoulli trials (binomial trials) with a success probability of p are performed n times in total,

Function to find the probability mass that the number of successes is x

f(x,n,p) = {}_n \mathrm{ C }_xp^x(1-p)^{ n-x } \quad (0 \leqq n;\ 0 \leqq x \leqq n;\ 0 \leqq p\leqq 1)\\

Function to find the lower cumulative probability of the number of successes x

P(n,x,p) = \sum_{i=0}^xf(i,n,p)

Function to find the upper cumulative probability of the number of successes x

P(n,x,p) = \sum_{i=x}^nf(i,n,p)

I wrote it in Python

import math
import numpy as np
import matplotlib.pyplot as plt

class ToolBox:

  def combination(total, chosen):
      return math.factorial(total) / math.factorial(chosen)/ math.factorial(total-chosen)

class BinomialDistribution:
  """
Generate a binomial distribution object with the total number of trials n and the probability of success p.

    Attributes
    ----------
    total : int
Total number of trials n.
    p_of_sccess : float
Probability of success in one trial p.
    p_of_fail : float
Failure probability in one trial 1-p.
  """

  def __init__(self, total, p_of_success):
    """
    Parameters
    ----------
    total : int
Total number of trials n.
    p_of_success : float
Probability of success in one trial p.
    """
    assert total > 0, "Condition error: 0 <= total"
    assert p_of_success >= 0 and p_of_success <= 1, "Condition error: 0 <= p_of_success <= 1"
    
    self.total = total
    self.p_of_sccess = p_of_success
    self.p_of_fail = 1 - p_of_success

  def get_probability_mass(self, success):
    """
Find the probability mass that succeeds x times

    Parameters
    ----------
    success : int
Number of successes x.

    Returns
    -------
    probability_mass : float
Probability mass of x.
    """
    assert success >= 0 and success <= self.total, "Condition error: 0 <= sccuess <= total"

    fail = self.total - success
    combination = ToolBox.combination(self.total, success)
    probability_mass = combination * (self.p_of_sccess ** success) * (self.p_of_fail) ** fail
    return probability_mass

  def get_lower_culmitive_distribution(self, success):
    """
Lower cumulative probability of x(Sum of probability masses from 0 to x times)Seeking.

    Parameters
    ----------
    success : int
Number of successes x.

    Returns
    -------
    result : float
Lower cumulative probability of x.
    """
    result = 0
    for i in range (0, success + 1):
      result += binomial_distribution.get_probability_mass(i)
    return result

  def get_upper_culmitive_distribution(self, success):
    """
Upper cumulative probability of x(x ~ sum of probability masses of all trials,)Seeking.

    Parameters
    ----------
    success : int
Number of successes x.

    Returns
    -------
    result : float
Upper cumulative probability of x.
    """
    result = 0
    for i in range (success, self.total + 1):
      result += binomial_distribution.get_probability_mass(i)
    return result

  def draw_graph(self):
    """
Draw a graph and save it in png format.
    """
    x = np.arange(0, self.total + 1, 1)
    y = []
    for i in range(0, self.total + 1):
      y.append(self.get_probability_mass(i))
    plt.plot(x, y)
    plt.savefig('graph.png')

Run

#10 trials, 0 success rate.Create a binomial distribution object of 5.
binomial_distribution = BinomialDistribution(10, 0.5)

#Get the probability mass for 2 successes.
print(binomial_distribution.get_probability_mass(2))

#Get the lower cumulative probability when the success probability is 2 times.
print(binomial_distribution.get_lower_culmitive_distribution(2))

#Get the upper cumulative probability when the success probability is 2 times.
print(binomial_distribution.get_upper_culmitive_distribution(2))

#Draw a graph of this binomial distribution.
binomial_distribution.draw_graph()

result

0.0439453125 #Probability mass when the number of successes is 2
0.0546875 #Lower cumulative probability with 2 success probabilities
0.9892578125 #Upper cumulative probability when the success probability is 2 times

I used this site to match the answers https://keisan.casio.jp/exec/system/1161228843

The graph is saved in the same directory.

April 7, 2020 Amendments

--Corrected the part that was called "Probability Density Function (PDF)" to "Probability Mass Function (PMF)". It seems that the latter is used when the random variable x (success in this case) is a discrete value. However, some sites and books use "probability density" for discrete binomial distributions, and I feel that they are not so strictly distinguished. --Added graph drawing function using Matplotlib --Fixed to separate the number of successes x (successs) from the constructor and specify it when calling the method. --Fixed a typo in the formula

Referenced site

How to write MathJax https://easy-copy-mathjax.nakaken88.com/

A site that calculates the binomial distribution https://keisan.casio.jp/exec/system/1161228843

Probability density function and probability mass function https://data-science.gr.jp/theory/tbs_pdf_and_pmf.html