Weibull-class             package:distr             R Documentation

_C_l_a_s_s "_W_e_i_b_u_l_l"

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

     The Weibull distribution with 'shape' parameter a, by default =1,
     and 'scale' parameter b has density given by, by default =1,

               d(x) = (a/b) (x/b)^(a-1) exp(- (x/b)^a)

     for x > 0.

     C.f. 'rweibull'

_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 'Weibull(shape,
     scale)'. This object is a Weibull 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 '"WeibullParameter"': the parameter of
          this distribution (shape and scale), declared at its
          instantiation 

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

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

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

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

_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 = "Weibull")': initialize method 

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

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

     _s_h_a_p_e 'signature(object = "Weibull")': returns the slot 'shape' of
          the parameter of the distribution 

     _s_h_a_p_e<- 'signature(object = "Weibull")': modifies the slot 'shape'
          of the parameter of the distribution 

_N_o_t_e:

     The density is d(x)=0 for x < 0.
      The cumulative is p(x) = 1 - exp(- (x/b)^a),
      the mean is E(X) = b Gamma(1 + 1/a),
      and the Var(X) = b^2 * (gamma(1 + 2/a) - (gamma(1 + 1/a))^2).

_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:

     'WeibullParameter-class' 'AbscontDistribution-class' 'Reals-class'
     'rweibull'

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

     W=Weibull(shape=1,scale=1) # W is a Weibull distribution with shape=1 and scale=1.
     r(W)(1) # one random number generated from this distribution, e.g. 0.5204105
     d(W)(1) # Density of this distribution is 0.3678794 for x=1.
     p(W)(1) # Probability that x<1 is 0.6321206.
     q(W)(.1) # Probability that x<0.1053605 is 0.1.
     shape(W) # shape of this distribution is 1.
     shape(W)=2 # shape of this distribution is now 2.

