关于圆内均匀分布的检验与估计

ON THE TESTING AND ESTIMATION OF UNIFORM DISTRIBUTION IN A CIRCLE

本文针对某型火箭炮武器系统试验中 ,提出的子母弹抛撒均匀性战术技术指标评定方法问题 ,假设子母弹子弹落点为圆内均匀分布 ,推导出了二维随机变量 (R ,Θ)的密度函数 g(r ,θ)和分布函数G(r ,θ)并讨论了其性质。采用了ω2 检验法对子弹分布均匀性进行检验 ,在此基础上 ,利用随机变量R的分布性质 ,推导出了等效半径Re 的估计公式及讨论了估计性质。为了描述子母弹抛撒的均匀性 。

This paper gives a method of assessing the tactical and technical indices of cartridge ejection uniformity It was proposed when testing some type of weapon systems On the supposition that points of fall of cartridges from a shrapnel have an uniform distribution in a circle, the density function g(r,θ) and distribution function G(r,θ) of two demensional random variable (R,Θ) , are derived and discussed The uniformity of distribution is tested with the ω 2 test method On the basis, and utilizing the nature of distribution of random variable R , is derived the formula for an equivalent radius R e and the estimated nature discussed In order to describe the uniformity of cartridges ejected, the analytical expression describing quantitatively the uniformity index J is given through the derivation