Fd-class

0th

Percentile

Class "Fd"

The F distribution with df1 = $n1$, by default = 1, and df2 = $n2$, by default = 1, degrees of freedom has density $$ d(x) = \frac{\Gamma(n_1/2 + n_2/2)}{\Gamma(n_1/2)\Gamma(n_2/2)} \left(\frac{n_1}{n_2}\right)^{n_1/2} x^{n_1/2 -1} \left(1 + \frac{n_1 x}{n_2}\right)^{-(n_1 + n_2) / 2}% $$ for $x > 0$.

C.f. rf

Keywords
distribution
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.

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< code=""> 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.

See Also

FParameter-class AbscontDistribution-class Reals-class rf

Aliases
  • Fd-class
  • Fd
  • initialize,Fd-method
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.
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...
Documentation reproduced from package distr, version 2.6, License: LGPL-3

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