Rayleigh                package:VGAM                R Documentation

_T_h_e _R_a_y_l_e_i_g_h _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 Rayleigh distribution with parameter 'a'.

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

     drayleigh(x, a)
     prayleigh(q, a)
     qrayleigh(p, a)
     rrayleigh(n, a)

_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.

       a: the parameter a.

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

     See 'rayleigh', the 'VGAM' family function for estimating the
     parameter a by maximum likelihood estimation, for the formula of
     the probability density function and range restrictions on the
     parameter a.

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

     'drayleigh' gives the density, 'prayleigh' gives the distribution
     function, 'qrayleigh' gives the quantile function, and 'rrayleigh'
     generates random deviates.

_N_o_t_e:

     The Rayleigh distribution is related to the Maxwell distribution.

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

     T. W. Yee

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

     Evans, M., Hastings, N. and Peacock, B. (2000) _Statistical
     Distributions_, New York: Wiley-Interscience, Third edition.

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

     'rayleigh', 'maxwell'.

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

     ## Not run: 
     a = 2
     x = seq(-1, 8, by=0.1)
     plot(x, drayleigh(x, a=a), type="l", ylim=c(0,1), las=1, ylab="",
          main="Rayleigh density divided into 10 equal areas; red=cdf")
     abline(h=0, col="blue", lty=2)
     qq = qrayleigh(seq(0.1,0.9,by=0.1),a=a)
     lines(qq, drayleigh(qq, a=a), col="purple", lty=3, type="h")
     lines(x, prayleigh(x, a=a), col="red")
     ## End(Not run)

