Posnorm                 package:VGAM                 R Documentation

_T_h_e _P_o_s_i_t_i_v_e-_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, distribution function, quantile function and random
     generation for the univariate positive-normal distribution.

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

     dposnorm(x, mean=0, sd=1)
     pposnorm(q, mean=0, sd=1)
     qposnorm(p, mean=0, sd=1)
     rposnorm(n, mean=0, sd=1)

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

    x, q: vector of quantiles.

       p: vector of probabilities.

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

mean, sd: see 'rnorm'. 

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

     See 'posnormal1', the 'VGAM' family function for estimating the
     parameters,  for the formula of the probability density function
     and other details.

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

     'dposnorm' gives the density, 'pposnorm' gives the distribution
     function, 'qposnorm' gives the quantile function, and 'rposnorm'
     generates random deviates.

_N_o_t_e:

     'rposnorm()' may run very slowly if the mean is very negative.

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

     T. W. Yee

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

     'posnormal1'.

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

     ## Not run: 
     m =  0.8
     x = seq(-1, 4, len=501)
     plot(x, dposnorm(x, m=m), type="l", ylim=0:1, las=1,
          ylab=paste("posnorm(m=",m,", sd=1)"), col="blue",
          main="Blue is density, red is cumulative distribution function",
          sub="Purple lines are the 10,20,...,90 percentiles")
     lines(x, pposnorm(x, m=m), col="red")
     abline(h=0)
     probs = seq(0.1, 0.9, by=0.1)
     Q = qposnorm(probs, m=m)
     lines(Q, dposnorm(Q, m=m), col="purple", lty=3, type="h")
     lines(Q, pposnorm(Q, m=m), col="purple", lty=3, type="h")
     abline(h=probs, col="purple", lty=3)
     pposnorm(Q, m=m) - probs # Should be all 0
     ## End(Not run)

