Frechet                 package:VGAM                 R Documentation

_T_h_e _F_r_e_c_h_e_t _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 three parameter Frechet distribution.

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

     dfrechet(x, location=0, scale=1, shape)
     pfrechet(q, location=0, scale=1, shape)
     qfrechet(p, location=0, scale=1, shape)
     rfrechet(n, location=0, scale=1, shape)

_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.

location, scale, shape: the location parameter a, scale parameter b,
          and shape parameter s.

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

     See 'frechet2' and 'frechet3', the 'VGAM' family functions for
     estimating the 2 (without location parameter) and 3 parameters by
     maximum likelihood estimation, for the formula of the probability
     density function and range restrictions on the parameters.

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

     'dfrechet' gives the density, 'pfrechet' gives the distribution
     function, 'qfrechet' gives the quantile function, and 'rfrechet'
     generates random deviates.

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

     T. W. Yee

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

     Castillo, E., Hadi, A. S., Balakrishnan, N. Sarabia, J. S. (2005)
     _Extreme Value and Related Models with Applications in Engineering
     and Science_, Hoboken, N.J.: Wiley-Interscience.

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

     'frechet2', 'frechet3'.

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

     ## Not run: 
     shape = 5
     x = seq(-0.1, 3.5, len=100)
     plot(x, dfrechet(x, shape=shape), type="l", ylab="", las=1,
          main="Frechet density divided into 10 equal areas; red=cdf")
     abline(h=0, col="blue", lty=2)
     qq = qfrechet(seq(0.1,0.9,by=0.1), shape=shape)
     lines(qq, dfrechet(qq, shape=shape), col="purple", lty=3, type="h")
     lines(x, pfrechet(q=x, shape=shape), col="red")
     ## End(Not run)

