R: Class "Fd"

Fd-class {distr} | R Documentation

## Class "Fd"

### Description

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 from the Class

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

### Slots

`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.

### Extends

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

### Methods

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

### Ad hoc methods

- 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.

### Note

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.

### Author(s)

Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de

### 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.
    ## 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...

[Package distr version 2.8.0 Index]