椭球等高分布族中T<sub>0</sub><sup>2</sup>的精确分布

椭球等高分布族中T₀²的精确分布

摘要: 设X～EC_p（u₁,Σ,φ）,即X服从椭球等高布分;X₁,X₂,…,X_m是来自X的样本,作 T_0^2=(\barX-u)^\prime \Sigma^-1(\barX-u), \quad\left(\barX=\frac1n \sum_i=1^n X_i\right)本文将在一定条件下,给出T₀²的密度函数。

Abstract: Let X be a p-dimension random variable, and X～EC_p（u₁,Σ,φ）,that is, the characteristic function of X is φ（（t-μ）’Σ（t-μ））,X₁,…,X_m are samples from X. In this paper we obtain the density function of T_0^2=(\barX-u)^\prime \Sigma^-1(\barX-u), \quad\left(\barX=\frac1n \sum_i=1^n X_i\right) under some assumptions.