Using Statistics to Test for Normality of Pi

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SUMMARY

The discussion focuses on testing the normality of the digits of π (pi) to determine if each digit occurs with equal frequency. A suggested method involves randomly sampling strings of size 20 and applying the Chi-squared goodness of fit test to assess uniform distribution. The results indicate that π exhibits normality up to 22.5 trillion decimal places in base 10 and an equivalent number in hexadecimal. The conversation also raises the question of whether normality is base-dependent, suggesting potential patterns in different numeral systems.

PREREQUISITES
  • Understanding of Chi-squared goodness of fit test
  • Familiarity with random sampling techniques
  • Knowledge of statistical normality concepts
  • Basic comprehension of numeral systems (base 10 and hexadecimal)
NEXT STEPS
  • Research the application of Chi-squared tests in statistical analysis
  • Explore methods for random sampling in statistical studies
  • Investigate the concept of normality in different numeral systems
  • Read the paper linked in the discussion for detailed methodologies and findings
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Statisticians, mathematicians, data analysts, and anyone interested in the properties of π and statistical testing methods.

WWGD
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Is there a " reasonable" way to test for the normality of ##\pi## , i .e., that every digit occurs with the same frequency? Someone suggested randomly sampling strings of size 20 and outputting the frequency. Then I guess we could average the frequencies among samples , use a chi-squared test. Assuming random sampling can be done, is this a sound way of testing?
 
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Yes. The Chi-squared goodness of fit test can be used to test if the digits are from a uniform distribution.
 
Is normality dependent upon the base - is it possible for there to be a pattern in one base that then appears random in another?

anyway, here is one method that showed normality out to 22.5 trillion base 10 decimal places and an equivalent number of hexideximal ones

https://arxiv.org/pdf/1612.00489.pdf
 
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