与F分布有关的二阶偏导数之性质

Characters of Second Order Partial Derivative Related to F Distribution

运用对无穷级数的一些运算组合及分析,并结合Γ函数对数微商公式,深入分析与Γ函数有关的一些特殊函数的性质,揭示了参数变化时F分布密度函数的极值先减后增的性质.本文的方法和结论在研究概率密度函数的性质时有重要作用,比如它可以判断密度曲线高度的变化趋势.

This paper uses the operation combinations and the analyses of infinite series, and applying logarithmic derivative formula of Γ function, analyses deeply the characters of some special functions about Γ function, reveals that the extreme value of F distributed density function reduces at the beginning and then increases when the parameter changes. The methods and conclusions of this paper are imporatant to research the characters of some probability density functions, for example, we can use it to decide the tendencies about the changes of height on density function.