Cauchy-class              package:distr              R Documentation

_C_l_a_s_s "_C_a_u_c_h_y"

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

     The Cauchy distribution with location l, by default =0, and scale
     s , by default =1,has density

                 f(x) = 1 / (pi s (1 + ((x-l)/s)^2))

     for all x. C.f. 'rcauchy'

_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 'Cauchy(location,
     scale)'. This object is a Cauchy distribution.

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

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

     '_p_a_r_a_m': Object of class '"CauchyParameter"': the parameter of
          this distribution (location and scale), declared at its
          instantiation 

     '_r': Object of class '"function"': generates random numbers (calls
          function 'rcauchy')

     '_d': Object of class '"function"': density function (calls
          function 'dcauchy')

     '_p': Object of class '"function"': cumulative function (calls
          function 'pcauchy')

     '_q': Object of class '"function"': inverse of the cumulative
          function (calls function 'qcauchy')

_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 = "Cauchy")': initialize method 

     _l_o_c_a_t_i_o_n 'signature(object = "Cauchy")': returns the slot
          'location' of the parameter of the distribution 

     _l_o_c_a_t_i_o_n<- 'signature(object = "Cauchy")': modifies the slot
          'location' of the parameter of the distribution 

     _s_c_a_l_e 'signature(object = "Cauchy")': returns the slot 'scale' of
          the parameter of the distribution 

     _s_c_a_l_e<- 'signature(object = "Cauchy")': modifies the slot 'scale'
          of the parameter of the distribution 

_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:

     'CauchyParameter-class' 'AbscontDistribution-class' 'Reals-class'
     'rcauchy'

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

     C=Cauchy(location=1,scale=1) # C is a Cauchy distribution with location=1 and scale=1.
     r(C)(1) # one random number generated from this distribution, e.g. 4.104603
     d(C)(1) # Density of this distribution is 0.3183099 for x=1.
     p(C)(1) # Probability that x<1 is 0.5.
     q(C)(.1) # Probability that x<-2.077684 is 0.1.
     location(C) # location of this distribution is 1.
     location(C)=2 # location of this distribution is now 2.

