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.
