F分布密度函数之性质

The Property of F Distribution Density Function

本文利用特殊函数的性质,较详细地分析了F分布密度函数之性质,指出了该密度函数与相应参数之间的关系.本文主要研究第二个参数变化对密度函数的影响,证明了n增大时F(m,n)分布的密度函数极大值也越来越大,还指出了n变化时F(m,n)分布的相应密度曲线与另一特定密度曲线交点的变化规律.

Applying some properties of special functions, this paper analysis fully the properties of F distribution density function and points out the relations between this density function and its parameter. This paper mainly studies the effects of change of the second parameter to density function, proves that the maximum of F（rn, n） distribution density function becomes more and more big when n is increasing, also points out the varying regularities of intersection points of F（rn, n） distribution density curve and some fixed density curve when n is varying.