lgammaUC                package:VGAM                R Documentation

_T_h_e _L_o_g-_G_a_m_m_a _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 log-gamma distribution with location parameter
     'location', scale parameter 'scale' and shape parameter 'k'.

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

     dlgamma(x, location=0, scale=1, k=1)
     plgamma(q, location=0, scale=1, k=1)
     qlgamma(p, location=0, scale=1, k=1)
     rlgamma(n, location=0, scale=1, k=1)

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

    x, q: vector of quantiles.

       p: vector of probabilities.

       n: number of observations. Positive integer of length 1.

location: the location parameter a.

   scale: the (positive) scale parameter b.

       k: the (positive) shape parameter k.

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

     See 'lgammaff', the 'VGAM' family function for estimating the one
     parameter standard log-gamma distribution by maximum likelihood
     estimation, for formulae and other details.  Apart from 'n', all
     the above arguments may be vectors and are recyled to the
     appropriate length if necessary.

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

     'dlgamma' gives the density, 'plgamma' gives the distribution
     function, 'qlgamma' gives the quantile function, and 'rlgamma'
     generates random deviates.

_N_o_t_e:

     The 'VGAM' family function 'lgamma3ff' is for the three parameter
     (nonstandard) log-gamma distribution.

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

     T. W. Yee

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

     Kotz, S. and Nadarajah, S. (2000) _Extreme Value Distributions:
     Theory and Applications_, pages 48-49, London: Imperial College
     Press.

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

     'lgammaff', 'prentice74'.

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

     ## Not run: 
     x = seq(-3.2, 5, by=0.01)
     loc = 1
     Scale = 1.5
     k = 1.4
     plot(x, dlgamma(x, loc, Scale, k), type="l", col="blue", ylim=c(0,1),
          main="Blue is density, red is cumulative distribution function",
          sub="Purple are 5,10,...,95 percentiles", las=1, ylab="")
     abline(h=0, col="blue", lty=2)
     lines(qlgamma(seq(0.05,0.95,by=0.05), loc, Scale, k), 
           dlgamma(qlgamma(seq(0.05,0.95,by=0.05), loc, Scale, k), loc, Scale, k),
           col="purple", lty=3, type="h")
     lines(x, plgamma(x, loc, Scale, k), type="l", col="red")
     abline(h=0, lty=2)
     ## End(Not run)

