pottwhitt              package:DCluster              R Documentation

_P_o_t_t_h_o_f_f-_W_h_i_t_t_i_n_g_h_i_l_l'_s _s_t_a_t_i_s_t_i_c _f_o_r _o_v_e_r_d_i_s_p_e_r_s_i_o_n

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

     This statistic can be used to test for homogeinity among all the
     relative risks. The test statistic is:


                     E_+ * sum_i [O_i(O_i-1)/E_i]


     If we supposse that the data are generated from a multinomial
     model, this is the locally U.M.P. when considering the next
     hypotheses:

       H_0  :  theta_1 = ... = theta_n)=lambda
       H_1  :  theta_i ~ Ga(lambda^2/sigma^2, lambda/sigma^2)

     Notice that in this case, lambda is supposed to be unknown. The
     alternative hypotheses means that relative risks come all from a
     Gamma distribution with mean lambda and variance sigma^2.

     _pottwhitt.stat_ is the function to calculates the value of the
     statistic for the data.

     _pottwhitt.boot_ is used when performing a non-parametric
     bootstrap.

     _pottwhitt.pboot_ is used when performing a parametric bootstrap.

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

     Potthoff, R. F. and Whittinghill, M.(1966). Testing for
     Homogeneity: I. The Binomial and Multinomial Distributions.
     Biometrika 53, 167-182.

     Potthoff, R. F. and Whittinghill, M.(1966). Testing for
     Homogeneity: The Poisson Distribution. Biometrika 53, 183-190.

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

     DCluster, pottwhitt.stat, pottwhitt.boot, pottwhitt.pboot

