loglapUC                package:VGAM                R Documentation

_T_h_e _L_o_g-_L_a_p_l_a_c_e _D_i_s_t_r_i_b_u_t_i_o_n

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

     Density, distribution function, quantile function and random
     generation for the 3-parameter log-Laplace distribution with
     location parameter 'location.ald', scale parameter 'scale.ald' (on
     the log scale), and asymmetry parameter 'kappa'.

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

     dloglap(x, location.ald=0, scale.ald=1,
             tau=0.5, kappa=sqrt(tau/(1-tau)), log=FALSE)
     ploglap(q, location.ald=0, scale.ald=1,
             tau=0.5, kappa=sqrt(tau/(1-tau)))
     qloglap(p, location.ald=0, scale.ald=1,
             tau=0.5, kappa=sqrt(tau/(1-tau)))
     rloglap(n, location.ald=0, scale.ald=1,
             tau=0.5, kappa=sqrt(tau/(1-tau)))

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

    x, q: vector of quantiles.

       p: vector of probabilities.

       n: number of observations. If 'length(n) > 1' then the length is
          taken to be the number required. 

location.ald, scale.ald: the location parameter xi and the (positive)
          scale parameter sigma, on the log scale. 

     tau: the quantile parameter tau. Must consist of values in (0,1).
          This argument is used to specify 'kappa' and is ignored if
          'kappa' is assigned.

   kappa: the asymmetry parameter kappa. Must consist of positive
          values. 

     log: if 'TRUE', probabilities 'p' are given as 'log(p)'. 

_D_e_t_a_i_l_s:

     A positive random variable Y is said to have a log-Laplace
     distribution if log(Y) has an asymmetric Laplace distribution
     (ALD). There are many variants of ALDs and the one used here is
     described in 'alaplace3'.

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

     'dloglap' gives the density, 'ploglap' gives the distribution
     function, 'qloglap' gives the quantile function, and 'rloglap'
     generates random deviates.

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

     T. W. Yee

_R_e_f_e_r_e_n_c_e_s:

     Kozubowski, T. J. and Podgorski, K. (2003) Log-Laplace
     distributions. _International Mathematical Journal_, *3*, 467-495.

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

     'dalap', 'alaplace3', 'loglaplace1'.

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

     x = seq(-0.2, 5, by=0.01)
     loc = 0; sigma = exp(0.5); kappa = 1
     ## Not run: 
     plot(x, dloglap(x, loc, sigma, kappa=kappa), type="l", col="blue",
          main="Blue is density, red is cumulative distribution function",
          ylim=c(0,1), sub="Purple are 5,10,...,95 percentiles", las=1, ylab="")
     abline(h=0, col="blue", lty=2)
     lines(qloglap(seq(0.05,0.95,by=0.05), loc, sigma, kappa=kappa),
           dloglap(qloglap(seq(0.05,0.95,by=0.05), loc, sigma, kappa=kappa),
                     loc, sigma, kappa=kappa), col="purple", lty=3, type="h")
     lines(x, ploglap(x, loc, sigma, kappa=kappa), type="l", col="red")
     abline(h=0, lty=2)
     ## End(Not run)
     ploglap(qloglap(seq(0.05,0.95,by=0.05), loc, sigma, kappa=kappa),
               loc, sigma, kappa=kappa)

