On the generalized multinomial distribution, optimal multinomialdetectors, and generalized weighted partial decision detectors

The probability of a particular outcome of a multinomial trial may depend on the trial number. The generalized multinomial distribution describes such an experiment. A mathematical statement of the generalized multinomial distribution is given. The Neyman-Pearson optimum generalized multinomial detectors for deterministic signals are derived for both binary and M-ary signaling. The equivalence of the generalized multinomial detectors and generalized weighted partial decision detectors is shown. The author claims that the work of E.K. Al-Hussaini (see ibid., vol.37, p.1099, 1989) on generalized multinomial detectors contains certain errors