Description Objects from the Class Slots Extends Methods Ad hoc methods Note Author(s) See Also Examples

The F distribution with `df1 =`

*n1*, by default `= 1`

,
and `df2 =`

*n2*, by default `= 1`

, degrees of freedom has density

*d(x) = Gamma((n1 + n2)/2) / (Gamma(n1/2) Gamma(n2/2))
(n1/n2)^(n1/2) x^(n1/2 - 1)
(1 + (n1/n2) x)^-(n1 + n2)/2*

for *x > 0*.

C.f. `rf`

Objects can be created by calls of the form `Fd(df1, df2)`

.
This object is a F distribution.

`img`

Object of class

`"Reals"`

: The space of the image of this distribution has got dimension 1 and the name "Real Space".`param`

Object of class

`"FParameter"`

: the parameter of this distribution (df1 and df2), declared at its instantiation`r`

Object of class

`"function"`

: generates random numbers (calls function rf)`d`

Object of class

`"function"`

: density function (calls function df)`p`

Object of class

`"function"`

: cumulative function (calls function pf)`q`

Object of class

`"function"`

: inverse of the cumulative function (calls function qf)`.withArith`

logical: used internally to issue warnings as to interpretation of arithmetics

`.withSim`

logical: used internally to issue warnings as to accuracy

`.logExact`

logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function

`.lowerExact`

logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function

`Symmetry`

object of class

`"DistributionSymmetry"`

; used internally to avoid unnecessary calculations.

Class `"AbscontDistribution"`

, directly.

Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.

Class `"Distribution"`

, by class `"AbscontDistribution"`

.

- initialize
`signature(.Object = "Fd")`

: initialize method- df1
`signature(object = "Fd")`

: returns the slot`df1`

of the parameter of the distribution- df1<-
`signature(object = "Fd")`

: modifies the slot`df1`

of the parameter of the distribution- df2
`signature(object = "Fd")`

: returns the slot`df2`

of the parameter of the distribution- df2<-
`signature(object = "Fd")`

: modifies the slot`df2`

of the parameter of the distribution

An ad hoc method is provided for slot

`d`

if`ncp!=0`

.For R Version

`<2.3.0`

ad hoc methods are provided for slots`q`

,`r`

if`ncp!=0`

; for R Version`>=2.3.0`

the methods from package stats are used.

It is the distribution of the ratio of the mean squares of n1 and n2 independent standard normals, and hence of the
ratio of two independent chi-squared variates each divided by its degrees of freedom. Since the ratio of a normal and the
root mean-square of m independent normals has a Student's *t_m* distribution, the square of a *t_m* variate has a F
distribution on 1 and m degrees of freedom.

The non-central F distribution is again the ratio of mean squares of independent normals of unit variance, but those in the numerator are allowed to have non-zero means and ncp is the sum of squares of the means.

Thomas Stabla [email protected],

Florian Camphausen [email protected],

Peter Ruckdeschel [email protected],

Matthias Kohl [email protected]

`FParameter-class`

`AbscontDistribution-class`

`Reals-class`

`rf`

1 2 3 4 5 6 7 8 9 10 11 | ```
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.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
df1(F) # df1 of this distribution is 1.
df1(F) <- 2 # df1 of this distribution is now 2.
Fn <- Fd(df1 = 1, df2 = 1, ncp = 0.5)
# Fn is a F distribution with df=1, df2=1 and ncp =0.5.
d(Fn)(1) ## from R 2.3.0 on ncp no longer ignored...
``` |

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