EBMDistribution           package:fOptions           R Documentation

_E_x_p_o_n_e_n_t_i_a_l _B_r_o_w_n_i_a_n _M_o_t_i_o_n _D_i_s_t_r_i_b_u_t_i_o_n_s

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

     A collection and description of distributions and  related
     functions which are useful in the theory of  exponential Brownian
     motion and Asian Option Valuation.  The functions compute
     densities and probabilities for  the log-Normal distribution, the
     Gamma distribution,  the Reciprocal-Gamma distribution, and the
     Johnson  Type-I distribution. Functions are made available for 
     the compution of moments including the Normal, the  log-Normal,
     the Reciprocal-Gamma, and the Asian-Option  Density. In addition a
     function is given to compute  numerically first and second
     derivatives of a given   function.    


     The functions are:

       'dlognorm'    the log-Normal density and derivatives,
       'plognorm'    the log-Normal, a synonyme for R's plnorm,
       'dgam'        the Gamma density, a synonyme for R's dgamma,
       'pgam'        the Gamma probability, a synonyme for R's pgamma,
       'drgam'       the Reciprocal-Gamma density,
       'prgam'       the Reciprocal-Gamma probability,
       'djohnson'    the Johnson Type I density,
       'pjohnson'    the Johnson Type I probability,
       'mnorm'       the Moments of Normal density,
       'mlognorm'    the Moments of log-Normal density,
       'mrgam'       the Moments of reciprocal-Gamma density,
       'masian'      the Moments of Asian Option density,
       'derivative'  the First and second numerical derivative.

_U_s_a_g_e:

     dlognorm(x, meanlog = 0, sdlog = 1, deriv = c(0, 1, 2))
     plognorm(q, meanlog = 0, sdlog = 1)
     dgam(x, alpha, beta, log = FALSE)
     pgam(q, alpha, beta, lower.tail = TRUE, log = FALSE)
     drgam(x, alpha, beta, deriv = c(0, 1, 2))
     prgam(q, alpha, beta, lower.tail = TRUE, log = FALSE)
     djohnson(x, a = 0, b = 1, c = 0, d = 1, deriv = c(0, 1, 2))
     pjohnson(q, a = 0, b = 1, c = 0, d = 1)

     mnorm(mean = 0, sd = 1)
     mlognorm(meanlog = 0, sdlog = 1)
     mrgam(alpha = 1/2, beta = 1)
     mjohnson(a, b, c, d)
     masian(Time = 1, r = 0.045, sigma = 0.30)

     derivative(x, y, deriv = c(1, 2))

_A_r_g_u_m_e_n_t_s:

a, b, c, d: [*johnson] - 
           the parameters of the Johnson Type I distribution. The
          default values are 'a=1', 'b=1', 'c=0', and 'd=1'. 

alpha, beta: [*gam] - 
           the parameters of the Gamma distribution.  

   deriv: an integer value, the degree of differentiation, either 0, 1 
          or 2. 

     log: a logical, if 'TRUE', densities and probabilities are given 
          on a logarithmic scale. 

lower.tail: a logical, if 'TRUE', the default, then the probabilities 
          are 'P[X <= x]', otherwise, 'P[X > x]'. 

mean, sd: [*lognorm] - 
           the parameters of the Normal distribution, the mean and the
          standard deviation respectively. The default values are
          'mean=0' and 'sd=1'. 

meanlog, sdlog: [*lognorm] - 
           the parameters of the Log Normal distribution, the mean and 
          the standard deviation respectively. The default values are
          'mean=0' and 'sd=1'.  

       q: a real numeric value or vector. 

Time, r, sigma: the parameters of the Asian Option distribution. 

       x: a real numeric value or vector. 

       y: [derivative] - 
           a real numeric value or vector, the function values from
          which to compute the first and second derivative. 

_V_a_l_u_e:

     The functions 'd*' and 'p*' return the values or  numeric vectors
     of the density and probability of the the  corresponding
     distribution.

     The functions 'm*' return a list with three elements,  the values
     of the first four moments 'rawMoments',  the values of the first
     four central moments 'centralMoments', and the skewness and
     kurtosis 'fisher', also called Fisher parameters. 

     The function 'derivative' returns a list of two elemtes,  '$x' and
     '$y', where '$y($x)' is either the first or second derivative of
     'y(x)' as selected by the argument 'deriv'.

_A_u_t_h_o_r(_s):

     Diethelm Wuertz for this R-Port.

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

     ## Examples:
        
     ## none ...

