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**2011/297**

**Title:**

NEW STATISTICAL BOX-TEST AND ITS POWER

**Authors:**
Igor Semaev, Mehdi M. Hassanzadeh

**Abstract:**

In this paper, statistical testing of N multinomial probabilities is studied and a new box-test, called \emph{Quadratic Box-Test}, is introduced. The statistics of the new test has \chi^2_s limit distribution as N and the number of trials n tend to infinity, where s is a parameter. The well-known empty-box test is a particular case for s=1. The proposal is quite different from Pearson’s goodness-of-fit test, which requires fixed N while the number of trials is growing, and linear box-tests. We prove that under some conditions on tested distribution the new test’s power tends to 1. That defines a wide region of non-uniform multinomial probabilities distinguishable from the uniform. For moderate N an efficient algorithm to compute the exact values of the first kind error probability is devised.

**ePrint:**
https://eprint.iacr.org/2011/297

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