distr (version 1.6)

Fd-class: Class "Fd"

Description

The F distribution with df1 = $n_1$, by default = 1, and df2 = $n_2$, by default = 1, degrees of freedom has density $$d(x)=\frac{\mathrm{\Gamma }(n_1/2+n_2/2)}{\mathrm{\Gamma }(n_1/2)\mathrm{\Gamma }(n_2/2)}{\left(\frac{n_1}{n_2}\right)}^{n_1/2}{x}^{n_1/2-1}{(1+\frac{n_{1}x}{n_2})}^{-(n_1+n_2)/2}$$ for $x > 0$. C.f. rf

Objects from the Class

Objects can be created by calls of the form Fd(df1, df2). This object is a F distribution.

Extends

Class "AbscontDistribution", directly. Class "UnivariateDistribution", by class "AbscontDistribution". Class "Distribution", by class "AbscontDistribution".

See Also

FParameter-class AbscontDistribution-class Reals-class rf

Examples

F=Fd(df1=1,df2=1) # F is a F distribution with df=1 and df2=1.
r(F)(1) # one random number generated from this distribution, e.g. 29.37863
d(F)(1) # Density of this distribution is 0.1591549 for x=1 .
p(F)(1) # Probability that x<1 is 0.5.
q(F)(.1) # Probability that x<0.02508563 is 0.1.
df1(F) # df1 of this distribution is 1.
df1(F)=2 # df1 of this distribution is now 2.