Fd-class {distr} | R Documentation |
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
:"Reals"
: The space of the image of this distribution has got dimension 1
and the name "Real Space". param
:"FParameter"
: the parameter of this distribution (df1 and df2),
declared at its instantiation r
:"function"
: generates random numbers (calls function rf)d
:"function"
: density function (calls function df)p
:"function"
: cumulative function (calls function pf)q
:"function"
: inverse of the cumulative function (calls function qf)
Class "AbscontDistribution"
, directly.
Class "UnivariateDistribution"
, by class "AbscontDistribution"
.
Class "Distribution"
, by class "AbscontDistribution"
.
signature(.Object = "Fd")
: initialize method signature(object = "Fd")
: returns the slot df1
of the parameter of the distribution signature(object = "Fd")
: modifies the slot df1
of the parameter of the distribution signature(object = "Fd")
: returns the slot df2
of the parameter of the distribution signature(object = "Fd")
: modifies the slot df2
of the parameter of the distribution d
if ncp!=0
.
<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 statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de,
Matthias Kohl Matthias.Kohl@stamats.de
FParameter-class
AbscontDistribution-class
Reals-class
rf
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...