poissonp                package:VGAM                R Documentation

_P_o_i_s_s_o_n-_p_o_i_n_t_s-_o_n-_a-_p_l_a_n_e/_v_o_l_u_m_e _D_i_s_t_a_n_c_e_s _D_i_s_t_r_i_b_u_t_i_o_n

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

     Estimating the density parameter of the distances from a fixed
     point to the u-th nearest point, in a plane or volume.

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

     poissonp(ostatistic, dimension=2, link="loge", earg=list(),
              idensity=NULL, method.init=1)

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

ostatistic: Order statistic. A single positive integer. For example,
          the value 5 means the response are the distances of the fifth
          nearest value to that point (usually over many planes or
          volumes).

dimension: The value 2 or 3; 2 meaning a plane and 3 meaning a volume.

    link: Parameter link function applied to the (positive) density
          parameter, called lambda below. See 'Links' for more choices.

    earg: List. Extra argument for the link. See 'earg' in 'Links' for
          general information.

idensity: Optional initial value for the parameter. A 'NULL' value
          means a value is obtained internally. Use this argument if
          convergence failure occurs.

method.init: An integer with value '1' or '2' which specifies the
          initialization method for lambda. If failure to converge
          occurs try another value and/or else specify a value for
          'idensity'.

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

     Suppose the number of points in any region of area A of the plane
     is a Poisson random variable with mean lambda*A (i.e., lambda is
     the _density_ of the points). Given a fixed point P, define D_1,
     D_2,... to be the distance to the nearest point to P, second
     nearest to P, etc.  This 'VGAM' family function estimates lambda
     since the probability density function for D_u is easily derived,
     u=1,2,....  Here, u corresponds to the argument 'ostatistic'.

     Similarly, suppose the number of points in any volume V is a
     Poisson random variable with mean lambda*V where, once again,
     lambda is the _density_ of the points. This 'VGAM' family function
     estimates lambda by specifying the argument 'ostatistic' and using
     'dimension=3'.

     The mean of D_u is returned as the fitted values. Newton-Raphson
     is the same as Fisher-scoring.

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

     An object of class '"vglmff"' (see 'vglmff-class'). The object is
     used by modelling functions such as 'vglm', 'rrvglm' and 'vgam'.

_W_a_r_n_i_n_g:

     Convergence may be slow if the initial values are far from the
     solution. This often corresponds to the situation when the
     response values are all close to zero, i.e., there is a high
     density of points.

     Formulae such as the means have not been fully checked.

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

     T. W. Yee

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

     'poissonff'.

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

     y = rgamma(n <- 10, shape=exp(-1))   # Not good data!
     os = 2
     fit = vglm(y ~ 1, poissonp(os, 2), tra=TRUE, cri="c")
     fit = vglm(y ~ 1, poissonp(os, 3), tra=TRUE, cri="c") # Slow convergence?
     fit = vglm(y ~ 1, poissonp(os, 3, idensi=1), tra=TRUE, cri="c")
     fitted(fit)[1:4]
     mean(y)
     coef(fit, matrix=TRUE)
     Coef(fit)

