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：本文考虑了统计复杂度函数的三种变体，该函数被用作信号-噪声混合中有用信号检测问题的准则。通过解析方法得到了最大化所考虑的统计复杂度变体的概率分布，并得出了关于使用哪种变体进行检测效率的结论。展示了所考虑的信息特征之间的比较，并通过合成信号示例说明了分析结果。提出了一种选择信息准则阈值的方法，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。阈值的选择先验地依赖于解析获得的最大值。结果表明，基于全变差的复杂度在有效信号检测能力上表现最佳。