Norm-class               package:distr               R Documentation

_C_l_a_s_s "_N_o_r_m"

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

     The normal distribution has density

       f(x) = 1/(sqrt(2 pi) sigma) e^-((x - mu)^2/(2 sigma^2))

     where mu is the mean of the distribution and sigma the standard
     deviation. C.f. 'rnorm'

_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 'Norm(mean, sd)'. This
     object is a normal distribution.

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

     '_i_m_g': Object of class '"Reals"': The domain of this distribution
          has got dimension 1 and the name "Real Space". 

     '_p_a_r_a_m': Object of class '"UniNormParameter"': the parameter of
          this distribution (mean and sd), declared at its
          instantiation 

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

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

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

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

_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:

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

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

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

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

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

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

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

     - 'signature(e1 = "Norm", e2 = "Norm")'

     + 'signature(e1 = "Norm", e2 = "Norm")':  For the normal
          distribution the exact convolution formulas are implemented
          thereby improving the general numerical approximation.

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

     _m_e_a_n 'signature(object = "Norm")': returns the slot 'mean' of the
          parameter of the distribution 

     _m_e_a_n<- 'signature(object = "Norm")': modifies the slot 'mean' of
          the parameter of the distribution 

     _s_d 'signature(object = "Norm")': returns the slot 'sd' of the
          parameter of the distribution  

     _s_d<- 'signature(object = "Norm")': modifies the slot 'sd' 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:

     'UniNormParameter-class' 'AbscontDistribution-class' 'Reals-class'
     'rnorm'

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

     N=Norm(mean=1,sd=1) # N is a normal distribution with mean=1 and sd=1.
     r(N)(1) # one random number generated from this distribution, e.g. 2.257783
     d(N)(1) # Density of this distribution is  0.3989423 for x=1.
     p(N)(1) # Probability that x<1 is 0.5.
     q(N)(.1) # Probability that x<-0.2815516 is 0.1.
     mean(N) # mean of this distribution is 1.
     sd(N)=2 # sd of this distribution is now 2.
     M=Norm() # M is a normal distribution with mean=0 and sd=1.
     O=M+N # O is a normal distribution with mean=1 (=1+0) and sd=sqrt(5) (=sqrt(2^2+1^2)).

