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n, m = data.shape mean = np.zeros((n, m)) M2 = np.zeros((n, m)) for i in range(m): if i == 0: delta = data - mean mean = mean + delta / (i + 1) M2 = delta * (data - mean) else: delta = data - mean mean = mean + delta / (i +
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x = np.arange(1, variances.shape + 1) ax1.semilogy(variances.T, linewidth=1) ax1.set_xlabel('Number of
Samples') ax1.set_ylabel('Variance') ax1.set_title('Running Sample Variances')
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ax2.semilogy(np.abs(mean.T), linewidth=1) ax2.set_xlabel('Number of
Samples') ax2.set_ylabel('Average (absolute value)') ax2.set_title('Running Sample Averages')
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For each column i, the difference delta between the current data point and the previous mean is calculated, and the mean and M2 are updated accordingly.
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Please help improve this media file by adding it to one or more categories, so it may be associated with related media files (
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391:{{subst:Please link images|File:Sample mean and variance of IID samples from a standard Cauchy distribution..png}} ~~~~
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If the file has been modified from its original state, some details may not fully reflect the modified file.
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In each iteration, the mean and M2 (the sum of the squares of differences from the mean) are updated.
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The following pages on the
English Knowledge (XXG) use this file (pages on other projects are not listed):
333:– If you remix, transform, or build upon the material, you must distribute your contributions under the
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cumsum = np.cumsum(data, axis=1) cum_n = np.arange(1, data.shape + 1) return cumsum / cum_n
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I, the copyright holder of this work, hereby publish it under the following license:
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Sample mean and variance of IID samples from a standard Cauchy distribution..png
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variances = running_sample_variance(data) mean = running_sample_average(data)
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sample mean and variance of IID samples from a standard Cauchy distribution.
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Uploaded while editing "Cauchy distribution" on en.wikipedia.org
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Click on a date/time to view the file as it appeared at that time.
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variance_n = M2 / (np.arange(1, m + 1)) return variance_n
148:""" Welford's online algorithm to calculate the variance.
142:```python import numpy as np import matplotlib.pyplot as plt
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n = 10 # Number of rows m = 500000 # Number of columns
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Creative
Commons Attribution-ShareAlike 4.0 International
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Add a one-line explanation of what this file represents
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Plot the running sample averages in the second subplot
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fig, (ax2, ax1) = plt.subplots(1, 2, figsize=(16, 5))
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Commons is a freely licensed media file repository.
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799:Matplotlib version3.7.1, https://matplotlib.org/
510:https://commons.wikimedia.org/User:Cosmia_Nebula
344:https://creativecommons.org/licenses/by-sa/4.0
186:data = np.random.standard_cauchy(size=(n, m))
161:1) M2 = M2 + delta * (data - mean)
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157:variance = M2 / np.arange(1, m + 1). """
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128:Description
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819:39.37 dpc
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262:Licensing
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72:image/png
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223:```
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
