多管火箭落点样本均值与方差的分布研究

Study on Sample Mean Value and Variance Distribution of Multiple Launch Rocket Falling Points

为了弄清楚多管火箭射程和密集度的分布特征,应用多元正态分布和矩阵分析理论,研究了多管火箭落点样本均值和方差的分布模型和它们相互独立的条件。得出的结论是:样本均值服从正态分布,样本方差由若干个服从卡方分布的随机变量的线性之和组成;样本均值的期望等于各管落点期望的算术平均值,方差为各管方差的算术平均值;样本方差是各管落点总体平均方差的无偏估计,方差与各管落点散布的差异相关;样本均值与方差相互独立的充要条件是:各管落点属于独立同分布样本。

In order to understand distribution characteristics of firing range and intensity of mutiple launch rocket （MLR）, sample mean value and variance distribution model of MLR falling points and their conditions of mutual independence were studied by means of multielement normal distribution and matrix analysis theory. Acquired conclusion was that the sample mean value submitted to normal distribution, and the sample variance was composed of a number of linear sum of random variable submitted to Chi-Squared distribution. The expectation of sample mean value is arithmetic mean value of MLR falling points, and variance is arithmetic mean value of MLR. The sample variance is the unbiased estimation of arithmetic mean value of MLR falling points, and the variance bears a relation to scatter difference of MLR falling points Only when falling points of MLR are independent from a common density, their sample mean value an variance are independent.