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The chi-square family of signal fluctuation distributions is defined. Rules are given for embedding the Swerling cases, and other cases of interest, in this family. Probability of detection curves are presented for the chi-square family of fluctuations, including cases whose probability of detection curves cannot be bracketed by the Swerling cases and the non-fluctuating case. The work of Weinstock has indicated such cases to be of practical interest; the fluctuation loss, for probability of detection exceeding 0.50, can be much larger than that for Swerling Case I. A discussion and partial analysis, accompanied by examples, is devoted to the question: when can the detection probability curves for signal fluctuations not belonging to the chi-square family be well approximated by curves resulting from chi-square fluctuations, and what methods can be used to choose adequately fitting chi-square fluctuation models when such a fit is possible?.
Peter Swerling (Tue,) studied this question.