File:Anscombe transform animated.gif
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Anscombe_transform_animated.gif (800 × 400 pixels, file size: 849 KB, MIME type: image/gif, looped, 51 frames, 4.1 s)
File information
Structured data
Captions
Summary
[edit]DescriptionAnscombe transform animated.gif |
English: ```python
import numpy as np import matplotlib.pyplot as plt import scipy import tempfile import os import imageio def anscombe_transform(samples, m): return 2 * np.sqrt(samples + 3/8) - (2*np.sqrt(m+3/8) - 1/(4*np.sqrt(m))) def plot_anscombe(m=10, n_samples=1000000): fig, axes = plt.subplot_mosaic("A", figsize=(8, 4)) ax1 = axes["A"] samples = anscombe_transform(np.random.poisson(m, n_samples), m) mean_diff = np.mean(samples) bins = sorted(list(set(samples))) # Plot the histogram of the samples ax1.hist(samples, bins=bins, align='right', rwidth=2, density=True) xs = np.linspace(-3.5, 3.5, 1000) ax1.plot(xs, scipy.stats.norm.pdf(xs)) ax1.vlines([mean_diff], 0,0.4, color='k') # Set the x-axis label and title ax1.set_xlabel('Number of Events') ax1.set_xlim(-4,+4) ax1.set_ylim(0, 0.44) ax1.set_title('Anscombe transform of Poisson(m)') text_lines = [r'$m =$' + f'{m}', r'$m^{3/2}\mu =$' + f'{m**1.5 * mean_diff:.2f}, ', r'$m^{2}(\sigma-1) =$' + f'{m**2 * (np.std(samples)-1):.2f}',] text_x = 0.03 text_y = 0.9 text_color = 'black' text_size = 12 for i, line in enumerate(text_lines): ax1.text(text_x, text_y-(i*0.08), line, color=text_color, fontsize=text_size, ha='left', va='bottom', transform=ax1.transAxes) fig.tight_layout() return fig def interpolate_counts(counts, frames_per_step): interpolated_counts = [counts[0]] for i in range(1,len(counts)): interval = (counts[i] - counts[i-1]) // i interpolated_counts += list(range(counts[i-1], counts[i], interval)) return interpolated_counts + [counts[-1]] with tempfile.TemporaryDirectory() as temp_dir: n_steps = 10 frames_per_step = 10 ms = interpolate_counts([2**n for n in range(n_steps)], frames_per_step) n_frames = len(ms)-1 for i in range(n_frames): fig = plot_anscombe(m=ms[i], n_samples=10000000) filename = os.path.join(temp_dir, f"plot_{i:03d}.png") fig.savefig(filename) plt.close(fig) # Compile images into GIF fps = 12 images = [] for i in range(n_frames): filename = os.path.join(temp_dir, f"plot_{i:03d}.png") images.append(imageio.imread(filename)) imageio.mimsave(f"Anscombe transform.gif", images, duration=1/fps)``` |
Date | |
Source | Own work |
Author | Cosmia Nebula |
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 08:09, 4 March 2023 | 800 × 400 (849 KB) | Cosmia Nebula (talk | contribs) | Uploaded own work with UploadWizard |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
File usage on other wikis
The following other wikis use this file:
- Usage on en.wikipedia.org