Quantile dotplot in python

quantile_dotplot.py

"""Quantile dotplot.

Based on R code from https://github.com/mjskay/when-ish-is-my-bus/blob/master/quantile-dotplots.md

Reference:

Matthew Kay, Tara Kola, Jessica Hullman, Sean Munson. When (ish) is My Bus?
User-centered Visualizations of Uncertainty in Everyday, Mobile Predictive Systems.
CHI 2016. DOI: 10.1145/2858036.2858558

---------------------------

MIT License

Copyright (c) 2018 Pamphile Tupui ROY

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
"""
import matplotlib.pyplot as plt
from matplotlib.patches import Circle
from matplotlib.collections import PatchCollection
import matplotlib.ticker as ticker
import numpy as np
from scipy.stats import lognorm

# Parameters
sample = 20
n_bins = 7
args = {'s': 0.2, 'scale': 11.4}
data = lognorm.rvs(size=10000, **args)
pdf = lognorm.pdf

# Evenly sample the CDF and do the inverse transformation (quantile function) to have x.
# probability of drawing a value less than x (i.e. P(X < x)) and the corresponding
# value of x to achieve that probability on the underlying distribution
p_less_than_x = np.linspace(1 / sample / 2, 1 - (1 / sample / 2), sample)
x = np.percentile(data, p_less_than_x * 100)  # Inverce CDF (ppf)

# Create bins
hist = np.histogram(x, bins=n_bins)
bins, edges = hist
radius = (edges[1] - edges[0]) / 2

# Plot
fig, ax = plt.subplots()

# Real PDF
x_ = np.linspace(0, 30, 100)
ax.plot(x_, pdf(x_, **args), 'r-', lw=5, alpha=0.6, label='lognorm pdf')
ax.set_ylabel('PDF')
ax.set_xlabel('Value')

# Dotplot
ax2 = ax.twinx()
patches = []
max_y = 0
for i in range(n_bins):
    x_bin = (edges[i + 1] + edges[i]) / 2
    y_bins = [(i + 1) * (radius * 2) for i in range(bins[i])]

    max_y = max(y_bins) if max(y_bins) > max_y else max_y

    for _, y_bin in enumerate(y_bins):
        circle = Circle((x_bin, y_bin), radius)
        patches.append(circle)

p = PatchCollection(patches, alpha=0.4)
ax2.add_collection(p)

# Axis tweek
y_scale = (max_y + radius) / max(pdf(x, **args))
ticks_y = ticker.FuncFormatter(lambda x, pos: '{0:g}'.format(x / y_scale))
ax2.yaxis.set_major_formatter(ticks_y)
ax2.set_yticklabels([])
ax2.set_xlim([min(x) - radius, max(x) + radius])
ax2.set_ylim([0, max_y + radius])
ax2.set_aspect(1)

plt.show()

This is an example