berdev               package:benchden               R Documentation

_2_8 _b_e_n_c_h_m_a_r_k _d_e_n_s_i_t_i_e_s _f_r_o_m _B_e_r_l_i_n_e_t/_D_e_v_r_o_y_e (_1_9_9_4)

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

     Density, distribution function, quantile function and random 
     generation for the 28 distributions from Berlinet/Devroye (1994).

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

     bberdev(dnum = 1)
     dberdev(x,dnum = 1)
     nberdev(dnum = 1)
     pberdev(q,dnum = 1)
     qberdev(p,dnum = 1)
     rberdev(n,dnum = 1)

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

    dnum: number of distribution as in Berlinet/Devroye (1994), Section
          3.2. 

     x,q: vector of quantiles.  

       p: vector of probabilities.  

       n: number of observations.  

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

     These functions implement the 28 distributions from Berlinet and
     Devroye (1994),  Section 3.2, which are:

     'dnum == 1'   "uniform" on [0,1] as in stats-package 

     'dnum == 2'   "exponential" as in stats-package 

     'dnum == 3'   "Maxwell"

     'dnum == 4'   "double exponential"

     'dnum == 5'   "logistic" as in stats-package

     'dnum == 6'   "Cauchy" as in stats-package

     'dnum == 7'   "extreme value" 

     'dnum == 8'   "infinite peak"

     'dnum == 9'   "Pareto"

     'dnum == 10'  "symmetric Pareto" 

     'dnum == 11'  "normal" as in stats-package  

     'dnum == 12'  "lognormal" 

     'dnum == 13'  "uniform scale mixture" 

     'dnum == 14'  "Matterhorn" 

     'dnum == 15'  "logarithmic peak"

     'dnum == 16'  "isosceles triangle"   

     'dnum == 17'  "beta 2,2" as in stats-package 

     'dnum == 18'  "chi-square 1" as in stats-package 

     'dnum == 19'  "normal cubed"

     'dnum == 20'  "inverse exponential"

     'dnum == 21'  "Marronite" 

     'dnum == 22'  "skewed bimodal" 

     'dnum == 23'  "claw"  

     'dnum == 24'  "smooth comb"

     'dnum == 25'  "caliper"           

     'dnum == 26'  "trimodal uniform" 

     'dnum == 27'  "sawtooth"

     'dnum == 28'  "bilogarithmic peak"

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

 dberdev: gives the density, 

 pberdev: gives the distribution function, 

 qberdev: gives the quantile function, and 

 rberdev: generates random deviates.

 nberdev: gives the name of the distribution.

 bberdev: Since evaluation of loss functions  in nonparametric density
          estimation often requires numerical  integration, 'bberdev' 
          returns a vector of points you should  generally take care
          not to integrate over, e.g. points where  the density is not
          continous or not differentiable.

_A_c_k_n_o_w_l_e_d_g_e_m_e_n_t:

     The authors thank Luc Devroye for providing his original
     implementation for testing purposes.

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

     Thoralf Mildenberger, Henrike Weinert and Sebastian Tiemeyer

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

     A. Berlinet and L. Devroye, "A comparison of kernel density
     estimates,"  Publications de l'Institut de Statistique de
     l'Universite de Paris,  vol. 38(3), pp. 3-59, 1994.  <URL:
     http://cg.scs.carleton.ca/~luc/devs.html>

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

     # histogram and true density of "Claw"-distribution
     hist(rberdev(1000,dnum=23),breaks=100, main = " ",freq=FALSE)
     lines(seq(-3,3,0.01),dberdev(seq(-3,3,0.01),dnum=23),col="blue",lwd=2)
     title(paste(nberdev(dnum=23)))

     # plot cdf of simulated data and the df of "Matterhorn"-distribution
     plot.stepfun(rberdev(100,dnum=14),do.points=TRUE,main="")
     lines(seq(-1,1,0.001),pberdev(seq(-1,1,0.001),dnum=14),col="blue")
     title(paste(nberdev(dnum=14)))

     # plot quantiles of "smooth comb"-distribution
     plot(qberdev(seq(0,1,0.01),dnum=24),t="l")
     title(paste(nberdev(dnum=24)))

