Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants of statistical complexity are obtained analytically and conclusions about the efficiency of using one or another variant for detection problem are made. The comparison of considered information characteristics is shown and analytical results are illustrated on an example of synthesized signals. A method is proposed for selecting the threshold of the information criterion, which can be used in decision rule for useful signal detection in the signal-noise mixture. The choice of the threshold depends a priori on the analytically obtained maximum values. As a result, the complexity based on the total variation demonstrates the best ability of useful signal detection.

翻译：本文研究了统计复杂度函数的三种变体，并将其用作信号-噪声混合中有用信号检测问题的判据。通过解析方法得到了最大化所考虑统计复杂度变体的概率分布，并对不同变体在检测问题中的有效性得出了结论。对比了所考虑的信息特征，并通过合成信号实例展示了解析结果。提出了一种选择信息判据阈值的方法，该阈值可用于信号-噪声混合中有用信号检测的决策规则中。阈值的选取先验地依赖于解析得到的最大值。结果表明，基于总变差的复杂度具有最佳的有用信号检测能力。