Maxwell                 package:VGAM                 R Documentation

_T_h_e _M_a_x_w_e_l_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 distribution function for the Maxwell distribution.

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

     dmaxwell(x, a)
     pmaxwell(q, a)
     qmaxwell(p, a)
     rmaxwell(n, a)

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

    x, q: vector of quantiles.

       p: vector of probabilities.

       n: number of observations. A single positive integer. 

       a: the parameter.

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

     See 'maxwell', the 'VGAM' family function for estimating the
     parameter a by maximum likelihood estimation, for the formula of
     the probability density function.

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

     'dmaxwell' gives the density, 'pmaxwell' gives the distribution
     function, 'qmaxwell' gives the quantile function, and 'rmaxwell'
     generates random deviates.

_N_o_t_e:

     The Maxwell distribution is related to the Rayleigh distribution.

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

     T. W. Yee

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

     Balakrishnan, N. and Nevzorov, V. B. (2003)  _A Primer on
     Statistical Distributions_. Hoboken, New Jersey: Wiley.

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

     'maxwell', 'Rayleigh', 'rayleigh'.

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

     ## Not run: 
     a = 3
     x = seq(-0.5, 3, len=100)
     plot(x, dmaxwell(x, a=a), type="l", col="blue", las=1, ylab="",
          main="blue is density, red is cumulative distribution function",
          sub="Purple lines are the 10,20,...,90 percentiles")
     abline(h=0, col="blue", lty=2)
     lines(x, pmaxwell(x, a=a), type="l", col="red")
     probs = seq(0.1, 0.9, by=0.1)
     Q = qmaxwell(probs, a=a)
     lines(Q, dmaxwell(Q, a), col="purple", lty=3, type="h")
     lines(Q, pmaxwell(Q, a), col="purple", lty=3, type="h")
     abline(h=probs, col="purple", lty=3)
     pmaxwell(Q, a) - probs    # Should be all zero
     ## End(Not run)

