A statistical measurement of randomness based on pattern vectors

Randomness of data or signals has been applied and studied in various theoretical and industrial fields. There are many ways to define and measure randomness. The most popular one probably is the statistical testing for randomness. Among the approaches adopted, Runs Test is a highly used technique in testing the randomness. In this article, we demonstrate the inefficient aspects of Runs Test and put forward a new approach, or pattern-vector-based statistic, based on pattern vectors that could effectively enhance the precision of testing randomness. A random binary sequence is supposedly to have less or no patterns. Based on this, we put forward our randomness-testing statistic. We also run an experiment to demonstrate how to apply this statistic and compare the efficiency or failure rate with Runs Test in dealing with a set of randomly generated input sequences. Moreover, we devise a statistically-justifiable measure of randomness for any given binary sequence. In the end, we demonstrate a way to combine this new device with Kalman filters to enhance the data assimilation. © 2020, North Atlantic University Union. All rights reserved.