Distribution of number of point targets killed and higher moments of coverage of area targets

The coverage C of area targets by salvos of weapons generally varies randomly, because of random target location and weapon impact point fluctuations. A third source of variation appears when, instead of an area target, a multiple‐element target is considered, consisting of m point targets distributed randomly and independently of one another around the target center. A multiple‐integral expression is derived for the probability pk of killing exactly k target elements. It is shown that pk is a linear function of the higher moments, of the order k to m, of the area coverage C. More explicit expressions are derived for the case of two weapons and for circular‐symmetric functions. Similar to well‐known results for the expectation and variance of coverage of area targets, these expressions can be evaluated by numerical quadrature. Furthermore, the coverage problem in which all underlying functions are Gaussian can be completely solved in closed form. For such a problem, with two weapons, numerical results are presented. They show that the distribution of k can be approximated by a binomial distribution only if the target center and weapon impact point fluctuations are small.