Nonparametric estimation of the CDF of weapon effectiveness on target performance

摘要

A military target is a system of K independent components X1,…, XK having distributions F1,…,FK, respectively. If a weapon is shot at this target, it will have a random effectiveness (destruction power) Xe with distribution Fe independent of the Xi's. Upon weapon impact, each component in the target sustains a random amount of damage and may still function but at a degraded level. The residual performance of component i is Yi = XiXe, i = 1,…,K having joint distribution G(y1,…,yKK). Data are usually collected on Yi's, and it is desired to use it to estimate Fe(x). In this investigation we show that if Fi(x) = (xT1)β,0⩽ x ⩽ Ti, i =1,…,K, then we canobtain a formula for Fe(x) in terms of G(y) and its probability density g(y). Thus, ifY1,…,Yn are data collected on residual target performance, one can use them to estimate Fe(x) or the average weapon effectiveness μe= ∫x0Fe(x)dx,whereF(x) =1− F(x). A kernel-type estimate of Fe(x) is presented, and its properties including the optimal choice of the window size are developed.