Table of contents
| Read No. | Name of chapter |
|---|---|
| 9 | Dunder Methods |
| 9 | Statistics - Probability |
Dunder Methods
What Are Dunder Methods?
In Python, special methods are a set of predefined methods you can use to enrich your classes. They are easy to recognize because they start and end with double underscores, for example init or str.
Object Initialization: __ init __:
To construct account objects from the Account class I need a constructor which in Python is the __ init __ dunder:
class Account:
"""A simple account class"""
def __init__(self, owner, amount=0):
"""
This is the constructor that lets us create
objects from this class
"""
self.owner = owner
self.amount = amount
self._transactions = []
The constructor takes care of setting up the object. In this case it receives the owner name, an optional start amount and defines an internal transactions list to keep track of deposits and withdrawals.
Object Representation: __ str __, __ repr __:
It’s common practice in Python to provide a string representation of your object for the consumer of your class (a bit like API documentation.) There are two ways to do this using dunder methods:
-
__ repr __: The “official” string representation of an object. This is how you would make an object of the class. The goal of __ repr __ is to be unambiguous.
-
__ str __: The “informal” or nicely printable string representation of an object. This is for the enduser.
class Account:
# ... (see above)
def __repr__(self):
return 'Account({!r}, {!r})'.format(self.owner, self.amount)
def __str__(self):
return 'Account of {} with starting amount: {}'.format(
self.owner, self.amount)
Operator Overloading for Comparing Accounts: __ eq __, __ lt __:
Why does > work equally well on integers, strings and other objects (as long as they are the same type)? This polymorphic behavior is possible because these objects implement one or more comparison dunder methods.
Callable Python Objects: __ call __:
You can make an object callable like a regular function by adding the call dunder method.
Statistics - Probability
What is probability?
At the most basic level, probability seeks to answer the question, “What is the chance of an event happening?” An event is some outcome of interest. To calculate the chance of an event happening, we also need to consider all the other events that can occur. The quintessential representation of probability is the humble coin toss.
From statistics to probability
Our data will be generated by flipping a coin 10 times and counting how many times we get heads. We will call a set of 10 coin tosses a trial. Our data point will be the number of heads we observe. We may not get the “ideal” 5 heads, but we won’t worry too much since one trial is only one data point. If we perform many, many trials, we expect the average number of heads over all of our trials to approach the 50%. The code below simulates 10, 100, 1000, and 1000000 trials, and then calculates the average proportion of heads observed.
import random
def coin_trial():
heads = 0
for i in range(100):
if random.random() <= 0.5:
heads +=1
return heads
def simulate(n):
trials = []
for i in range(n):
trials.append(coin_trial())
return(sum(trials)/n)
simulate(10)
>>> 5.4
simulate(100)
>>> 4.83
simulate(1000)
>>> 5.055
simulate(1000000)
>>> 4.999781
he coin_trial function is what represents a simulation of 10 coin tosses. It uses the random() function to generate a float between 0 and 1, and increments our heads count if it’s within half of that range. Then, simulate repeats these trials depending on how many times you’d like, returning the average number of heads across all of the trials. The coin toss simulations give us some interesting results.
First, the data confirm that our average number of heads does approach what probability suggests it should be. Furthermore, this average improves with more trials. In 10 trials, there’s some slight error, but this error almost disappears entirely with 1,000,000 trials. As we get more trials, the deviation away from the average decreases. Sound familiar? Sure, we could have flipped the coin ourselves, but Python saves us a lot of time by allowing us to model this process in code. As we get more and more data, the real-world starts to resemble the ideal.
The data and the distribution
The normal distribution refers to a particularly important phenomenon in the realm of probability and statistics.The normal distribution looks like this: Normal Distribution Look:
