t1lmoments             package:Lmoments             R Documentation

_T_r_i_m_m_e_d _L-_m_o_m_e_n_t_s

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

     Calculates sample trimmed L-moments with trimming parameter 1.

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

     t1lmoments(data,rmax=4)

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

    data: matrix or data frame.

    rmax: maximum order of trimmed L-moments.

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

     array of trimmed L-moments (trimming parameter = 1) up to order 4
     containing a row for each variable in data.

_N_o_t_e:

     Functions 'link{Lmoments}' and 'link{Lcoefs}' calculate trimmed
     L-moments if you specify 'trim=c(1,1)'.

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

     Juha Karvanen juha.karvanen@ktl.fi

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

     Karvanen, J. 2005. Estimation of quantile mixtures via L-moments
     and trimmed L-moments,  _Computational Statistics & Data
     Analysis_, in press, <URL:
     http://www.bsp.brain.riken.jp/publications/2005/karvanen_quantile_
     mixtures.pdf>.

     Elamir, E. A., Seheult, A. H. 2003. Trimmed L-moments, 
     _Computational Statistics & Data Analysis_ *43*, 299-314.

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

     'Lmoments' for L-moments, and  'dcauchypoly' and
     't1lmom2cauchypoly4' for the Cauchy-polynomial quantile mixture

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

     #Generates 500 random variables from the Cauchy-polynomial quantile mixture, 
     #calculates the trimmed L-moments,
     #estimates parameters via trimmed L-moments and 
     #plots the true pdf and the estimated pdf together with the histogram of the data.
     true_params<-t1lmom2cauchypoly4(c(0,1,0.075,0.343));
     x<-rcauchypoly(500,true_params);
     t1lmom<-t1lmoments(x);
     estim_params<-t1lmom2cauchypoly4(t1lmom);
     plotpoints<-seq(-10,10,by=0.01);
     histpoints<-c(seq(min(x)-1,-20,length.out=50),seq(-10,10,by=0.5),seq(20,max(x)+1,length.out=50));
     hist(x,breaks=histpoints,freq=FALSE,xlim=c(-10,10));
     lines(plotpoints,dcauchypoly(plotpoints,estim_params),col='red');
     lines(plotpoints,dcauchypoly(plotpoints,true_params),col='blue');

