PA 1.7: Classy Distributions¶
CEGM1000 MUDE: Week 1.7. Due: complete this PA prior to class on Friday, Oct 18, 2024.
Overview of Assignment¶
This assignment will help you understand more about Object Oriented Programming (OOP) in Python, by exploring how it's used in Scipy. In Python, OOP is done through classes, so you'll learn a bit about how classes can be useful and how to define and instantiate them. You will also learn about subclassing, otherwise known as inheritance, which is the ability for one (child) class to inherit the properties of another (parent) class.
Part 1: Playing with subclasses¶
We'll start by looking at some simple code that shows all the basics: defining a class, instantiating classes and inheritance. You're not required to do anything with it, but feel free to change this and play around!
class Person:
def __init__(self, name):
self.name = name
def say_hello(self):
print(f"Hey, I'm {self.name}, nice to meet you!")
class Employee(Person):
known_salaries = {"janitor": 50000, "professor": 100, "trader": 100000}
def __init__(self, name, job):
super().__init__(name)
self.job = job
def salary(self):
if self.job.lower() in self.known_salaries:
print(f"My salary is ${self.known_salaries[self.job.lower()]}!")
else:
print("I'm not too sure what my salary is :(")
class Friend(Person):
def say_hello(self):
print("Yoo, how are you doing? It's lovely to see you again :)")
def greet_person(person):
person.say_hello()
print(f"Hey {person.name}!")
james = Person("James")
james.say_hello()
print()
emma = Employee("Emma", "Janitor")
emma.salary()
emma.say_hello()
print()
philip = Friend("Philip")
greet_person(philip)
print()
greet_person(emma)
Notice that Emma can say hello, but James doesn't have a salary! The children class extends the parent. Confused about the __init__ or self? Go check out the reading! Also notice that since the Friend subclass and Employee subclasses both have say_hello, we can use either one in the greet_person function. You'll use this princople to complete Task 1.1.
Part 2: Inheritance and Distributions¶
In this part we will use inheritance to create our own custom distribution using the parent class scipy.stats.rv_continuous!
First we will define a function to help make plots easily, then we will confirm we can create a distribution. Finally, you will implement your own child class of scipy.stats.rv_continuous.
Task 1.1: Below there's some code that takes a distribution from Scipy and plots it. Read it to understand what it does, then run the cell so that we can use it later.
# DO NOT TOUCH ANYTHING IN THIS CODE CELL!
import scipy.stats
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
def plot_distribution(distribution, x_bounds = (-5, 5), function="pdf"):
X_LOW, X_HIGH = x_bounds
x_axis = np.linspace(X_LOW, X_HIGH, num=1000)
distribution_function = None
if function == "pdf":
distribution_function = distribution.pdf
elif function == "cdf":
distribution_function = distribution.cdf
else:
raise KeyError(f"{function} function not supported")
y_axis = np.vectorize(distribution_function)(x_axis)
plt.figure(figsize=(15, 5))
plt.plot(x_axis, y_axis)
plt.title("PDF of distribution")
plt.xlabel("x")
plt.xticks(np.linspace(X_LOW, X_HIGH, num=((X_HIGH - X_LOW) * 2 + 1)))
plt.ylabel("f(x)")
plt.show()
return x_axis, y_axis
In Scipy all distributions are children of the same parent class rv_continous. Read the documentation to get a feeling for what this parent class defines. One method it defines is the .pdf method, so if we just rely on that, we can freely swap between children classes!
Task 1.2: Below there's some code that takes a Normal distribution from Scipy and plots it, using our function. Pretty cool, right?
Test your understanding of this distribution by changing the standard deviation to 3 instead of 1. Does the figure respond as expected?
distribution = scipy.stats.norm(loc = 1)
x_axis, y_axis = plot_distribution(distribution)
Task 1.3: Complete the code below to create your own Uniform distribution from 1 to 3 and use the plotting function to confirm you have done it correctly.
At this point, it becomes important that you understand what a continuous parametric distribution is. If you have no idea what we are talking about, it is time to read the theory textbook chapters for this week!
distribution = scipy.stats.uniform(YOUR_CODE_HERE)
x_axis, y_axis = plot_distribution(distribution)
Part 3: Making a subclass¶
No let's see if we can define our own distribution! We can do this by creating a subclass of rv_continous. Reading documentation can be difficult to begin with, but try and see if you can think of how this would be done.
Task 3.1: Complete the implementation of the subclass below, so that the pdf is defined as follows: \begin{equation} f(x)= \begin{cases} 0.1 & \text{if } 0 < x < 3.6 \\ 2(x-5) & 5 < x < 5.8 \\ 0 & \text{elsewhere} \end{cases} \end{equation}
You don't need to worry about the scale or loc parameters we used earlier.
class new_distribution(YOUR_CODE_HERE):
""" A new piece-wise distribution."""
def _pdf(self, x):
""" f(x) =
0.1 when 0 < x < 3.6
2(x - 5) when 5 < x < 5.8
"""
YOUR_CODE_HERE # MORE THAN ONE LINE!
return YOUR_CODE_HERE
There is an IntegrationWarning that appears when integrating this PDF, which we can supress as follows. This works here on the last step, but you should use it with caution in other applications!
import warnings
warnings.simplefilter("ignore")
Task 3.2:
Use the plotting function to check that you implemented the class correctly. You need to do this by instantiating the class in the missing piece of code.
plot_distribution(YOUR_CODE_HERE, x_bounds = (0, 6))
plot_distribution(YOUR_CODE_HERE, x_bounds = (0, 6), function="cdf")
print()
Even the CDF of our custom distribution works! There's a lot of magic that can be accomplished with classes, which you won't need to known for MUDE, but this foundation will help you understand it the day you do!
