AbscontDistribution-class       package:distr       R Documentation

_C_l_a_s_s "_A_b_s_c_o_n_t_D_i_s_t_r_i_b_u_t_i_o_n"

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

     The 'AbscontDistribution'-class is the mother-class of the classes
     'Beta', 'Cauchy',  'Chisq', 'Exp', 'F', 'Gamma', 'Lnorm', 'Logis',
     'Norm', 'T', 'Unif' and  'Weibull'. Further absolutely continuous
     distributions can be defined either by declaration of own random
     number generator, density, cumulative distribution and quantile
     functions, or as result of a  convolution of two absolutely
     continuous distributions or by application of a mathematical
     operator to an absolutely continuous distribution. An additional
     way is, to specify only the random number generator. The function
     'RtoDPQ' then  approximates the three remaining slots d, p and q
     by random sampling.

_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
     'new("AbscontDistribution", r, d, p, q)'. The result of this call
     is an absolutely continuous distribution.

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

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

     '_p_a_r_a_m': Object of class '"Parameter"': the parameter of this
          distribution, having only  the slot name "Parameter of an
          absolutely continuous distribution" 

     '_r': Object of class '"function"': generates random numbers

     '_d': Object of class '"function"': density function

     '_p': Object of class '"function"': cumulative distribution
          function

     '_q': Object of class '"function"': quantile function

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

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

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

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

     _M_a_t_h 'signature(x = "AbscontDistribution")': application of a
          mathematical function, e.g. 'sin' or 'exp' (does not work
          with 'log'!), to this absolutely continouos distribution

     - 'signature(e1 = "AbscontDistribution")': application of `-' to
          this absolutely continuous distribution

     * 'signature(e1 = "AbscontDistribution", e2 = "numeric")':
          multiplication of this absolutely continuous  distribution by
          an object of class `numeric'

     / 'signature(e1 = "AbscontDistribution", e2 = "numeric")':
          division of this absolutely continuous  distribution by an
          object of class `numeric'

     + 'signature(e1 = "AbscontDistribution", e2 = "numeric")':
          addition of this absolutely continuous  distribution to an
          object of class `numeric'

     - 'signature(e1 = "AbscontDistribution", e2 = "numeric")':
          subtraction of an object of class `numeric' from this
          absolutely continuous distribution 

     * 'signature(e1 = "numeric", e2 = "AbscontDistribution")':
          multiplication of this absolutely continuous  distribution by
          an object of class `numeric'

     + 'signature(e1 = "numeric", e2 = "AbscontDistribution")':
          addition of this absolutely continuous  distribution to an
          object of class `numeric'

     - 'signature(e1 = "numeric", e2 = "AbscontDistribution")':
          subtraction of this absolutely continuous  distribution from
          an object of class `numeric'

     + 'signature(e1 = "AbscontDistribution", e2 =
          "AbscontDistribution")': Convolution of two absolutely
          continuous distributions. The slots p, d and q are
          approximated by grids.

     - 'signature(e1 = "AbscontDistribution", e2 =
          "AbscontDistribution")': Convolution of two absolutely
          continuous distributions. The slots p, d and q are
          approximated by grids.

     _p_l_o_t 'signature(object = "AbscontDistribution")': plots density,
          cumulative distribution and quantile  function 

_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:

     'Parameter-class' 'UnivariateDistribution-class' 'Beta-class'
     'Cauchy-class' 'Chisq-class' 'Exp-class' 'Fd-class' 'Gamma-class'
     'Lnorm-class' 'Logis-class' 'Norm-class' 'Td-class' 'Unif-class'
     'Weibull-class' 'DiscreteDistribution-class' 'Reals-class'
     'RtoDPQ'

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

     N = Norm() # N is a normal distribution with mean=0 and sd=1.
     E = Exp() # E is an exponential distribution with rate=1.
     A1 = E+1 # a new absolutely continuous distributions with exact slots d, p, q
     A2 = A1*3 # a new absolutely continuous distributions with exact slots d, p, q
     A3 = N*0.9 + E*0.1 # a new absolutely continuous distribution with approximated slots d, p, q
     r(A3)(1) # one random number generated from this distribution, e.g. -0.7150937
     d(A3)(0) # The (approximated) density for x=0 is 0.4379882.
     p(A3)(0) # The (approximated) probability that x <= 0 is 0.4562021.
     q(A3)(.1) # The (approximated) 10 percent quantile is 0.1.

