Testing the Fairness of a Coin by Akaike's Information Criterion

Takezawa, Kunio (2019) Testing the Fairness of a Coin by Akaike's Information Criterion. Journal of Advances in Mathematics and Computer Science, 34 (2). pp. 1-12. ISSN 2456-9968

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Abstract

In this paper, AIC (Akaike's Information Criterion) is used to judge whether a coin is biased or not using the sequence of heads and tails produced by tossing the coin several times. It is well known that AIC·(−0:5) is an efficient estimator of the expected log-likelihood when the true distribution is contained in a specified parametric model. In the coin tossing problem, however, AIC·(−0:5) works as an efficient estimator even if the true distribution is not contained in a specied parametric model. Moreover, the judgement of fairness of coin using AIC is equivalent to a statistical test using the Bernoulli distribution with a signicance level ranging from 11% to 18%. This indicates that the judgement of the fairness of coin based on AIC leads to a higher probability of type I errors than that given by a statistical test with a signicance level of 5%. These findings show that we judge the fairness of a coin based on AIC when we do not have any prior knowledge about its fairness and we want to judge it from the standpoint of prediction. In contrast, a statistical test with a significance level of 5% is adopted when we have prior knowledge that the coin is probably unbiased. Moreover, a statistical test with a 5% significance level allows us to conclude that the coin is biased if we obtain sufficient evidence that permits us to disbelieve the prior knowledge.

Item Type: Article
Subjects: Open Research Librarians > Mathematical Science
Depositing User: Unnamed user with email support@open.researchlibrarians.com
Date Deposited: 07 Apr 2023 07:43
Last Modified: 18 May 2024 07:23
URI: http://stm.e4journal.com/id/eprint/586

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