Matplotlib Logit Scale Plotting

Introduction

In this lab, we will learn how to create plots with logit axes in Matplotlib. Logit axes are commonly used in probability plots to represent the cumulative distribution function (CDF) of a distribution. We will use the math, numpy, and matplotlib.pyplot libraries for this lab.

VM Tips

After the VM startup is done, click the top left corner to switch to the Notebook tab to access Jupyter Notebook for practice.

Sometimes, you may need to wait a few seconds for Jupyter Notebook to finish loading. The validation of operations cannot be automated because of limitations in Jupyter Notebook.

If you face issues during learning, feel free to ask Labby. Provide feedback after the session, and we will promptly resolve the problem for you.

Import the necessary libraries and set up the data

We will import the math, numpy, and matplotlib.pyplot libraries and set up the data for the plots.

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

xmax = 10
x = np.linspace(-xmax, xmax, 10000)
cdf_norm = [math.erf(w / np.sqrt(2)) / 2 + 1 / 2 for w in x]
cdf_laplacian = np.where(x < 0, 1 / 2 * np.exp(x), 1 - 1 / 2 * np.exp(-x))
cdf_cauchy = np.arctan(x) / np.pi + 1 / 2

Create a plot with logit scale and standard notation

We will create a plot with logit scale and standard notation. This can be done by setting the y-axis scale to logit using set_yscale("logit") and setting the y-axis limits using set_ylim(). We will also plot the cumulative distribution functions for the normal, Laplacian, and Cauchy distributions using plot() and add a legend using legend().

fig, axs = plt.subplots(nrows=1, ncols=1, figsize=(6.4, 4.8))

axs.plot(x, cdf_norm, label=r"$\mathcal{N}$")
axs.plot(x, cdf_laplacian, label=r"$\mathcal{L}$")
axs.plot(x, cdf_cauchy, label="Cauchy")
axs.set_yscale("logit")
axs.set_ylim(1e-5, 1 - 1e-5)
axs.legend()
axs.grid()

plt.show()

Create a plot with logit scale and survival notation

We will create a plot with logit scale and survival notation. This can be done by setting the y-axis scale to logit and setting the one_half parameter to "1/2" and use_overline parameter to True using set_yscale("logit", one_half="1/2", use_overline=True)". We will also plot the cumulative distribution functions for the normal, Laplacian, and Cauchy distributions using plot() and add a legend using legend().

fig, axs = plt.subplots(nrows=1, ncols=1, figsize=(6.4, 4.8))

axs.plot(x, cdf_norm, label=r"$\mathcal{N}$")
axs.plot(x, cdf_laplacian, label=r"$\mathcal{L}$")
axs.plot(x, cdf_cauchy, label="Cauchy")
axs.set_yscale("logit", one_half="1/2", use_overline=True)
axs.set_ylim(1e-5, 1 - 1e-5)
axs.legend()
axs.grid()

plt.show()

Create a plot with linear scale

We will create a plot with linear scale. This can be done by simply plotting the cumulative distribution functions for the normal, Laplacian, and Cauchy distributions using plot() and add a legend using legend().

fig, axs = plt.subplots(nrows=1, ncols=1, figsize=(6.4, 4.8))

axs.plot(x, cdf_norm, label=r"$\mathcal{N}$")
axs.plot(x, cdf_laplacian, label=r"$\mathcal{L}$")
axs.plot(x, cdf_cauchy, label="Cauchy")
axs.legend()
axs.grid()

plt.show()

Summary

In this lab, we learned how to create plots with logit axes in Matplotlib. We created plots with logit scale and standard notation, logit scale and survival notation, and linear scale. We used the math, numpy, and matplotlib.pyplot libraries for this lab.