Fd-class                package:distr                R Documentation

_C_l_a_s_s "_F_d"

_D_e_s_c_r_i_p_t_i_o_n:

     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'

_O_b_j_e_c_t_s _f_r_o_m _t_h_e _C_l_a_s_s:

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

_S_l_o_t_s:

     '_i_m_g': Object of class '"Reals"': The space of the image of this
          distribution has got dimension 1 and the name "Real Space". 

     '_p_a_r_a_m': 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)

_E_x_t_e_n_d_s:

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

_M_e_t_h_o_d_s:

     _i_n_i_t_i_a_l_i_z_e 'signature(.Object = "Fd")': initialize method 

     _d_f_1 'signature(object = "Fd")': returns the slot 'df1' of the
          parameter of the distribution 

     _d_f_1<- 'signature(object = "Fd")': modifies the slot 'df1' of the
          parameter of the distribution 

     _d_f_2 'signature(object = "Fd")': returns the slot 'df2' of the
          parameter of the distribution 

     _d_f_2<- 'signature(object = "Fd")': modifies the slot 'df2' of the
          parameter of the distribution 

_N_o_t_e:

     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.

_A_u_t_h_o_r(_s):

     Thomas Stabla Thomas.Stabla@uni-bayreuth.de,
      Florian Camphausen Florian.Camphausen@uni-bayreuth.de,
      Peter Ruckdeschel Peter.Ruckdeschel@uni-bayreuth.de,
      Matthias Kohl Matthias.Kohl@uni-bayreuth.de

_S_e_e _A_l_s_o:

     'FParameter-class' 'AbscontDistribution-class' 'Reals-class' 'rf'

_E_x_a_m_p_l_e_s:

     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.

