Abstract: This paper analyses deeply certain properties of special function, and uses these properties to discuss the relation between the positions of F distribution density curves with different parameters. Besides, this paper discusses certain asymptotic properties of density curve and builds some related equations. As the application and verifications of conclusions, this paper gives some representative examples. The analytic methods of this paper can also be used to discuss certain properties about density curves of other distributions.

Key words: F distribution, Density curve, Parameter, \Gamma function