Appendix N — Overview of Project

Table of contents

• N.1 Using scipy.stats Objects

For the project deliverable in this class, you will create a “webapp” using streamlit.

The purpose of the “app” will be to provide a tool for fitting histograms to statistical data. The interface should include:

• A way for users to enter data. This should include:
  • A data entry area for users to enter data by hand
  • An option to upload data in the form of a CSV file
• The ability to fit multiple different types of distributions, such as normal, gamma, weibull, and other miscillaneous types.
  • Each distribution object in scipy has a fitting function, which returns the relevant parameters.
  • Your app should provide at least 10 different options
• A visualization of the data and the fitted distribution (i.e. a graph)
• An output area that shows the fitting parameters with some information about the quality of the fit (e.g. average error or maximum error between data and curve).
• The app should also provide a ‘manual fitting’ option, where users can adjust sliders to control the various parameters of the current distribution.
• The layout, such as use of tabs, columns, expanders, etc are up to you, but marks will be given for ‘esthetic appeal’ and clean layout.
• The app should be contained to a single page (so avoid the use of Streamlit’s multipage option), and uploaded as a .py file to the LEARN Dropbox.
• Bonus marks will be given to students who post their app on Github, and deploy it to the Streamlit Community Cloud
• You are welcome to use genAI to assist with this project. You can get access to many coding agents if you use Co-Pilot in VSCode. Access is free through the University, though I can’t quite recall how to set that up.

Figure N.1: Distributions are everywhere

N.1 Using scipy.stats Objects

The scipy.stats module contains many distributions which can be used to either generate data that follows a distribution, or to fit a distribution to given data. In this project we’ll use the latter approach. This approach is actually pretty straight-forward, as demonstrated below.

First let’s generate some data using a gamma distribution with parameters of 5, 1, 1.

import numpy as np
from scipy.stats import gamma
import matplotlib.pyplot as plt

data = gamma.rvs(5, 1, 1, size=1000)
fig, ax = plt.subplots(figsize=[5, 5])
ax.plot(data, 'k.')
ax.set_xlabel('Measurement Number')
ax.set_ylabel('Value')
ax.set_ylim([0, 25])

Now we can fit the gamma distribution to the data, and it should return the same parameters we used to generate the data.

params = gamma.fit(data)
print(params)

(np.float64(4.74709076626095), np.float64(1.132154490735322), np.float64(1.0403836667561777))

Now let’s generate some values using the gamma distribution with the fitted parameters and overlay in on the original data.

dist = gamma(*params)
x = np.linspace(0, 25, 100)
fit = dist.pdf(x)

fig, ax = plt.subplots(figsize=[5, 5])
ax.plot(x, fit)
ax.hist(data, bins=25, density=True);  
# The semi colon stops matplotlib from writing to the console