密度函数高度之变化

Some Changes of Height on Density Function

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,指出了第二个参数的变化对密度曲线的影响.关于其密度函数曲线,一个显著的特点是随着第二个参数的增大,密度曲线极大点的位置越来越高.另一个特点是当第一个参数固定而第二个参数不同时,二密度曲线或者只有一个交点,或者有两个交点.在第一种情况下,较大参数所对应的曲线在交点以前低于较小参数所对应的曲线,而在交点以后则高于之.在第二种情况下,较大参数所对应的曲线中间部分高于较小参数所对应的曲线,而两端则低于之.

This paper uses the properties of special functions, analyses properties of F distributed density function in detail, points out the effects of change of the second parameter on density curve. To say it in the main, about F density function curve, one remarkable characteristic is that in pace with the increase of the second parameter, the position of maximum point of density curve is more and more high. Another characteristic is that when the first parameter is fixed and the second is different, the two density curves have either one or two intersection points. In the first case, before intersection point, the curve which is belonged to the bigger parameter is lower than the curve which is belonged to the smaller parameter, and after intersection point, the former is higher that the latter. In the second case, the middle of the curve which is belonged to the bigger parameter is higher than the middle of the curve which is belonged to the smaller parameter, and about the others of the curve, the former is lower than the latter.