参数的变化对F分布密度函数之影响

该文运用对无穷级数的一些特殊处理方法,深入分析了与Γ函数有关的一些特殊函数的性质,揭示了参数变化时F分布密度函数极值变化的一些深刻规律.该文指明,n增大时F分布的密度函数f_{m,n}(x)的极大值单调增加,而m增大时该密度函数的极大值或单调减少,或先减后增.

The Effects of Changes of Parameters on Distribution Density Function

This paper uses some special treating methods of infinite series, analyses deeply the characters of some special functions about Γ function, reveals some profound regularities of the changes about the extreme value of F distribution density function when parameters change. This paper points out that the maximum of F distribution density function f_{m,n}(x) is monotone increasing when n increases, and the maximum of this density function is monotone decreasing, or decreases at the beginning and then increases when m increases.