Polono                 package:VGAM                 R Documentation

_T_h_e _P_o_i_s_s_o_n _L_o_g_n_o_r_m_a_l _D_i_s_t_r_i_b_u_t_i_o_n

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

     Density, and random generation for the Poisson lognormal
     distribution.

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

     dpolono(x, meanlog=0, sdlog=1, ...)
     rpolono(n, meanlog=0, sdlog=1)

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

       x: vector of quantiles.

       n: number of observations. Must be a positive integer of length
          1.

meanlog, sdlog : the mean and standard deviation of the normal
          distribution (on the log scale). They match the arguments in 
          'Lognormal'.

     ...: Arguments passed into  'integrate'.

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

     The Poisson lognormal distribution is similar to the negative
     binomial in that it can be motivated by a Poisson distribution
     whose mean parameter comes from a right skewed distribution (gamma
     for the negative binomial and lognormal for the Poisson lognormal
     distribution).

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

     'dpolono' gives the density, and 'rpolono' generates random
     deviates.

_N_o_t_e:

     'dpolono' involves numerical integration that is performed using
     'integrate'. Consequently, computations may be very slow. Also,
     numerical problems may occur, and if so, then the use of '...' may
     be needed.

     For the maximum likelihood estimation of the 2 parameters a 'VGAM'
     family function called 'polono', say, has not been written yet.

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

     T. W. Yee

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

     'lognormal', 'poissonff', 'negbinomial'.

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

     ## Not run: 
     meanlog = 0.5; sdlog = 0.5
     y = 0:19
     proby = dpolono(y, m=meanlog, sd=sdlog)
     plot(y, proby, type="h", col="blue", las=1, ylab="P[Y=y]", log="",
          main=paste("Poisson lognormal(meanlog=",meanlog,", sdlog=",sdlog,")",
                     sep=""))
     sum(proby)  # Should be 1

     y = rpolono(n=1000, m=meanlog, sd=sdlog)
     table(y)
     hist(y, breaks=((-1):max(y))+0.5, prob=TRUE)
     ## End(Not run)

