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.

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Skills Graph

%%%%{init: {'theme':'neutral'}}%%%% flowchart RL matplotlib(("`Matplotlib`")) -.-> matplotlib/BasicConceptsGroup(["`Basic Concepts`"]) matplotlib(("`Matplotlib`")) -.-> matplotlib/PlottingDataGroup(["`Plotting Data`"]) matplotlib(("`Matplotlib`")) -.-> matplotlib/PlotCustomizationGroup(["`Plot Customization`"]) python(("`Python`")) -.-> python/BasicConceptsGroup(["`Basic Concepts`"]) python(("`Python`")) -.-> python/ControlFlowGroup(["`Control Flow`"]) python(("`Python`")) -.-> python/DataStructuresGroup(["`Data Structures`"]) python(("`Python`")) -.-> python/ModulesandPackagesGroup(["`Modules and Packages`"]) python(("`Python`")) -.-> python/PythonStandardLibraryGroup(["`Python Standard Library`"]) python(("`Python`")) -.-> python/DataScienceandMachineLearningGroup(["`Data Science and Machine Learning`"]) matplotlib/BasicConceptsGroup -.-> matplotlib/importing_matplotlib("`Importing Matplotlib`") matplotlib/BasicConceptsGroup -.-> matplotlib/figures_axes("`Understanding Figures and Axes`") matplotlib/PlottingDataGroup -.-> matplotlib/line_plots("`Line Plots`") matplotlib/PlotCustomizationGroup -.-> matplotlib/legend_config("`Legend Configuration`") matplotlib/PlotCustomizationGroup -.-> matplotlib/grid_config("`Grid Configuration`") python/BasicConceptsGroup -.-> python/booleans("`Booleans`") python/ControlFlowGroup -.-> python/for_loops("`For Loops`") python/ControlFlowGroup -.-> python/list_comprehensions("`List Comprehensions`") python/DataStructuresGroup -.-> python/lists("`Lists`") python/DataStructuresGroup -.-> python/tuples("`Tuples`") python/DataStructuresGroup -.-> python/sets("`Sets`") python/ModulesandPackagesGroup -.-> python/importing_modules("`Importing Modules`") python/ModulesandPackagesGroup -.-> python/standard_libraries("`Common Standard Libraries`") python/PythonStandardLibraryGroup -.-> python/math_random("`Math and Random`") python/DataScienceandMachineLearningGroup -.-> python/numerical_computing("`Numerical Computing`") python/DataScienceandMachineLearningGroup -.-> python/data_visualization("`Data Visualization`") subgraph Lab Skills matplotlib/importing_matplotlib -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} matplotlib/figures_axes -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} matplotlib/line_plots -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} matplotlib/legend_config -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} matplotlib/grid_config -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} python/booleans -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} python/for_loops -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} python/list_comprehensions -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} python/lists -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} python/tuples -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} python/sets -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} python/importing_modules -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} python/standard_libraries -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} python/math_random -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} python/numerical_computing -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} python/data_visualization -.-> lab-48812{{"`Matplotlib Logit Scale Plotting`"}} end

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.