pLausen94              package:maxstat              R Documentation

_A_p_p_r_o_x_i_m_a_t_i_n_g _M_a_x_i_m_a_l_l_y _S_e_l_e_c_t_e_d _S_t_a_t_i_s_t_i_c_s

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

     Approximates the probability that a maximally selected rank
     statistic is greater or equal to 'b'.

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

     pLausen94(b, N, minprop=0.1, maxprop=0.9, m=NULL)
     qLausen94(p, N, minprop=0.1, maxprop=0.9, m=NULL)

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

       b: quantile. 

       p: probability. 

       N: number of observations.

 minprop: at least 'minprop'*100% of the observations in the first
          group. 

 maxprop: not more than 'minprop'*100% of the observations in the first
          group. 

       m: a integer vector containing the sample sizes in the first
          groups for each cutpoint considered. If 'is.null(m)' a
          continuous predictor is assumed. 

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

     Approximation based on an improved Bonferroni inequality.

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

     The probability that, under the hypothesis of independence, a
     maximally selected statistic greater equal 'b' is observed.

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

     Worsley, K.J. (1982), An Improved Bonferroni Inequality and
     Applications. _Biometrika_, *69*, 297-302

     Lausen, B. (1990), Maximal Selektierte Rangstatistiken.
     Dissertation.  Universit\"at Dortmund 

     Lausen, B., Sauerbrei, W. & Schumacher, M. (1994). Classification
     and Regression Trees (CART) used for the exploration of prognostic
     factors measured on different scales. in: P. Dirschedl & R.
     Ostermann (Eds), _Computational Statistics_, Heidelberg,
     Physica-Verlag, 483-496

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

     p <- pLausen94(2.5, 20, 0.25, 0.75)

     # Lausen 94, page 489

     if (round(p, 3) != 0.073) stop("error checking pLausen94")

     # the same

     p2 <- pLausen94(2.5, 200, 0.25, 0.75, m=seq(from=50, to=150, by=10))

     stopifnot(all.equal(round(p,3), round(p2,3)))

