Nbinom-class              package:distr              R Documentation

_C_l_a_s_s "_N_b_i_n_o_m"

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

     The negative binomial distribution with 'size' = n, by default =1,
     and 'prob' = p, by default =0.5, has density

             d(x) = Gamma(x+n)/(Gamma(n) x!) p^n (1-p)^x

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

     This represents the number of failures which occur in a sequence
     of Bernoulli trials before a target number of successes is
     reached. C.f. 'rnbinom'

_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 'Nbinom(prob, size)'.
     This object is a negative binomial 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 '"NbinomParameter"': the parameter of
          this distribution (prob, size), declared at its instantiation 

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

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

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

     '_q': Object of class '"function"': inverse of the cumulative
          function (calls function 'qnbinom'). 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 = "Nbinom")': initialize method 

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

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

     _s_i_z_e 'signature(object = "Nbinom")': returns the slot 'size' of
          the parameter of the distribution 

     _s_i_z_e<- 'signature(object = "Nbinom")': modifies the slot 'size' 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:

     'NbinomParameter-class' 'DiscreteDistribution-class'
     'Naturals-class' 'rnbinom'

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

     N=Nbinom(prob=0.5,size=1) # N is a binomial distribution with prob=0.5 and size=1.
     r(N)(1) # one random number generated from this distribution, e.g. 3
     d(N)(1) # Density of this distribution is  0.25 for x=1.
     p(N)(0.4) # Probability that x<0.4 is 0.5.
     q(N)(.1) # x=0 is the smallest value x such that p(B)(x)>=0.1.
     size(N) # size of this distribution is 1.
     size(N)=2 # size of this distribution is now 2.

