Geom-class               package:distr               R Documentation

_C_l_a_s_s "_G_e_o_m"

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

     The geometric distribution with 'prob' = p has density

                           p(x) = p (1-p)^x

     for x = 0, 1, 2, ...

     C.f. 'rgeom'

_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 'Geom(prob)'. This
     object is a geometric distribution.

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

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

     '_p_a_r_a_m': Object of class '"GeomParameter"': the parameter of this
          distribution (prob), declared at its instantiation

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

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

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

     '_q': Object of class '"function"': inverse of the cumulative
          function (calls function qgeom). The quantile is defined as
          the smallest value x such that F(x) >= p, where F is the
          distribution function.      

     '_s_u_p_p_o_r_t': Object of class '"numeric"': a (sorted) vector
          containing the support of the discrete density function

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

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

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

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

     _p_r_o_b 'signature(object = "Geom")': returns the slot prob of the
          parameter of the distribution

     _p_r_o_b<- 'signature(object = "Geom")': modifies the slot prob of the
          parameter of the distribution

_N_o_t_e:

     Working with a computer, we use a finite interval as support which
     carries at least mass (1-TruncQuantile).

_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:

     'GeomParameter-class' 'DiscreteDistribution-class'
     'Naturals-class' 'rgeom'

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

     G <- Geom(prob = 0.5) # G is a geometric distribution with prob = 0.5.
     r(G)(1) # one random number generated from this distribution, e.g. 0
     d(G)(1) # Density of this distribution is 0.25 for x = 1.
     p(G)(1) # Probability that x<1 is 0.75.
     q(G)(.1) # x = 0 is the smallest value x such that p(G)(x) >= 0.1.
     prob(G) # prob of this distribution is 0.5.
     prob(G) <- 0.6 # prob of this distribution is now 0.6.

