File:Binomial confidence band.svg
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Summary
| Description |
English: Illustration of confidence bands using simulated data. |
| Date | |
| Source |
Own work |
| Author | Skbkekas |
| Other versions |
[]
|
| SVG development |  This plot was created with Matplotlib. |
| Source code | Python codeimport numpy as np
import matplotlib.pyplot as plt
import scipy.special as sp
X = np.arange(18, 81, 2)
P = 1/(1+np.exp(1-0.2*np.sqrt(X-18)))
Y,S,n = [],[],500
for i,x in enumerate(X):
y = 1*(np.random.uniform(size=n)<P[i])
p = y.mean()
Y.append(p)
S.append(np.sqrt(p*(1-p)/n))
Y = np.array(Y)
S = np.array(S)
## Multiplier for 95% simultaneous confidence band using Bonferroni method.
f = -sp.ndtri(0.025/len(P))
plt.clf()
a = plt.plot(X, Y, '-', color='black')
plt.hold(True)
b = plt.plot(X, Y+2*S, '-', color='royalblue')
plt.plot(X, Y-2*S, '-', color='royalblue')
c = plt.plot(X, Y+f*S, '-', color='orangered')
plt.plot(X, Y-f*S, '-', color='orangered')
d = plt.plot(X, P, '-', color='green')
plt.ylim(0,1)
plt.xlim(18,80)
B = plt.legend((a,b,c,d), ('Estimate', '95% point-wise CB',\
'95% simultaneous CB', "True proportions"),\
'upper left')
B.draw_frame(False)
plt.xlabel("Age")
plt.ylabel("Proportion supporting candidate A")
plt.savefig("binomial_confidence_band.png")
plt.savefig("binomial_confidence_band.svg")
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Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution 3.0 Unported 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.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 04:11, 11 April 2009 | | 720 × 540 (43 KB) | Skbkekas | Added the line for true proportions. |
| 04:02, 11 April 2009 |  | 720 × 540 (41 KB) | Skbkekas | {{Information |Description={{en|1=Illustration of confidence bands using simulated data.}} |Source=Own work by uploader |Author=Skbkekas |Date=April 11, 2009 |Permission= |other_versions= }} <!--{{ImageUpload|full}}--> |
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