Beta-class               package:distr               R Documentation

_C_l_a_s_s "_B_e_t_a"

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

     The Beta distribution with parameters 'shape1' = a and 'shape2' =
     b has density

           Gamma(a+b)/(Gamma(a)Gamma(b))x^(a-1)(1-x)^(b-1)

     for a > 0, b > 0 and 0 <= x <= 1 where the boundary values at x=0
     or x=1 are defined as by continuity (as limits).

     C.f. 'rbeta'

_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 'Beta(shape1,
     shape2)'. This object is a beta 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 '"BetaParameter"': the parameter of this
          distribution (shape1 and shape2), declared at its
          instantiation 

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

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

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

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

_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 = "Beta")': initialize method

     _s_h_a_p_e_1 'signature(object = "Beta")': returns the slot shape1 of
          the parameter of the distribution

     _s_h_a_p_e_1<- 'signature(object = "Beta")': modifies the slot shape1 of
          the parameter of the distribution

     _s_h_a_p_e_2 'signature(object = "Beta")': returns the slot shape2 of
          the parameter of the distribution

     _s_h_a_p_e_2<- 'signature(object = "Beta")': modifies the slot shape2 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:

     'BetaParameter-class' 'AbscontDistribution-class' 'Reals-class'
     'rbeta'

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

     B <- Beta(shape1 = 1, shape2 = 1)
     # B is a beta distribution with shape1 = 1 and shape2 = 1.
     r(B)(1) # one random number generated from this distribution, e.g. 0.6979795
     d(B)(1) # Density of this distribution is 1 for x=1.
     p(B)(1) # Probability that x < 1 is 1.
     q(B)(.1) # Probability that x < 0.1 is 0.1.
     shape1(B) # shape1 of this distribution is 1.
     shape1(B) <- 2 # shape1 of this distribution is now 2.

