extreme                 package:evd                 R Documentation

_D_i_s_t_r_i_b_u_t_i_o_n_s _o_f _M_a_x_i_m_a _a_n_d _M_i_n_i_m_a

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

     Density function, distribution function, quantile function and
     random generation for the maximum/minimum of a given number of
     independent variables from a specified distribution.

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

     dextreme(x, densfun, distnfun, ..., distn, mlen = 1, largest = TRUE,
         log = FALSE)
     pextreme(q, distnfun, ..., distn, mlen = 1, largest = TRUE,
         lower.tail = TRUE) 
     qextreme(p, quantfun, ..., distn, mlen = 1, largest = TRUE,
         lower.tail = TRUE) 
     rextreme(n, quantfun, ..., distn, mlen = 1, largest = TRUE) 

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

    x, q: Vector of quantiles.

       p: Vector of probabilities.

       n: Number of observations.

densfun, distnfun, quantfun: Density, distribution and quantile
          function of the specified distribution. The density function
          must have a 'log' argument (a simple wrapper can always be
          constructed to achieve this).

     ...: Parameters of the specified distribution.

   distn: A character string, optionally given as an alternative to
          'densfun', 'distnfun' and 'quantfun' such that the density,
          distribution and quantile functions are formed upon the
          addition of the prefixes 'd', 'p' and 'q' respectively.

    mlen: The number of independent variables.

 largest: Logical; if 'TRUE' (default) use maxima, otherwise minima.

     log: Logical; if 'TRUE', the log density is returned.

lower.tail: Logical; if 'TRUE' (default) probabilities are P[X <= x],
          otherwise  P[X > x].

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

     'dextreme' gives the density function, 'pextreme' gives the
     distribution function and 'qextreme' gives the quantile function
     of the maximum/minimum of 'mlen' independent variables from a
     specified distibution. 'rextreme' generates random deviates.

_S_e_e _A_l_s_o:

     'rgev', 'rorder'

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

     dextreme(2:4, dnorm, pnorm, mean = 0.5, sd = 1.2, mlen = 5)
     dextreme(2:4, distn = "norm", mean = 0.5, sd = 1.2, mlen = 5)
     dextreme(2:4, distn = "exp", mlen = 2, largest = FALSE)
     pextreme(2:4, distn = "exp", rate = 1.2, mlen = 2)
     qextreme(seq(0.9, 0.6, -0.1), distn = "exp", rate = 1.2, mlen = 2)
     rextreme(5, qgamma, shape = 1, mlen = 10)
     p <- (1:9)/10
     pexp(qextreme(p, distn = "exp", rate = 1.2, mlen = 1), rate = 1.2)
     ## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

