par2cdf2               package:lmomco               R Documentation

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

     This function computes the nonexceedance probability of a given
     quantile from the weighted combination of two quantile functions.
     The distributions are specified by the two parameter object
     arguments. The left-tail parameter object is the distribution
     governing the left tail; the right-tail parameter object is the
     distribution governing the right tail. The quantile function
     algebra is


    Q(F) = (1-F) times Q_{lefttail}(F) + F times Q_{righttail}(F)


     where Q(F) is the equivalent quantile for nonexceedance
     probability F computed by the tail weigthing. Q_{lefttail}(F) is
     the left-tail quantile function; Q_{righttail} is the right-tail
     quantile function. The 'par2cdf2' function inverses the above
     equation for F. Parameter objects are discussed in 'vec2par' and
     'lmom2par' functions. If the optional 'weight' argument is
     provided, then the multiplication of '1-F' or 'F' is replaced by
     '1-weight' or 'weight', respectively. If 'weight=0', then the
     quantiles for the right tail are returned, and if 'weight=1', then
     the quantiles for the left tail are returned.

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

     par2cdf2(x,leftpara,rightpara,weight=NULL,...)

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

       x: A real value.

leftpara: The left-tail parameters from 'lmom2par' or similar.

rightpara: The right-tail parameters from 'lmom2par' or similar.

  weight: An optional weighting argument to use in lieu of 'F'.

     ...: The additional arguments are passed to the cumulative
          distribution function such as 'paracheck=FALSE' for the
          generalized Lambda distribution ('cdfgld').

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

     Nonexceedance probability (0 <= F <= 1) for 'x' from the two
     distributions.

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

     W.H. Asquith

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

     'par2cdf', 'lmom2par', and 'par2qua2'

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

     # Contrived example
     lmr       <- lmom.ub(rnorm(20))
     leftpara  <- parnor(lmr)
     rightpara <- pargev(lmr)
     combined.median <- par2qua2(0.5,leftpara,rightpara)
     combined.nonexceed <- par2cdf2(combined.median,leftpara,rightpara)

