meplot                 package:VGAM                 R Documentation

_M_e_a_n _E_x_c_e_s_s _P_l_o_t

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

     Mean excess plot (also known as a mean residual life plot), a
     diagnostic plot for the generalized  Pareto distribution (GPD).

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

     meplot(object, ...)
     meplot.default(y, main="Mean Excess Plot",
         xlab="Threshold", ylab="Mean Excess", lty=c(2,1:2),
         conf=0.95, col=c("blue","black","blue"), type="l", ...)
     meplot.vlm(object, ...)

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

       y: A numerical vector. 'NA's etc. are not allowed.

    main: Character. Overall title for the plot. 

    xlab: Character. Title for the x axis. 

    ylab: Character. Title for the y axis. 

     lty: Line type. The second value is for the mean excess value, the
          first and third values are for the envelope surrounding the
          confidence interval.

    conf: Confidence level. The default results in approximate 95
          percent confidence intervals for each mean excess value. 

     col: Colour of the three lines. 

    type: Type of plot. The default means lines are joined between the
          mean excesses and also the upper and lower limits of the
          confidence intervals. 

  object: An object that inherits class '"vlm"', usually of class
          'vglm-class' or 'vgam-class'. 

     ...: Graphical argument passed into 'plot'. See 'par' for an
          exhaustive list. The arguments 'xlim' and 'ylim' are
          particularly useful. 

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

     If Y has a GPD with scale parameter sigma and shape parameter
     xi<1, and if y>0, then

                 E(Y-u|Y>u) = frac{sigma+xi u}{1-xi}.

     It is a linear function in u, the threshold. Note that Y-u is
     called the _excess_ and values of Y greater than u are called
     _exceedences_. The empirical versions used by these functions is
     to use sample means to estimate the left hand side of the
     equation. Values of u in the plot are the values of y itself. If
     the plot is roughly a straight line then the GPD is a good fit;
     this plot can be used to select an appropriate threshold value.
     See 'gpd' for more details. If the plot is flat then the data may
     be exponential, and if it is curved then it may be Weibull or
     gamma.

     The function 'meplot' is generic, and 'meplot.default' and
     'meplot.vlm' are some methods functions for mean excess plots.

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

     A list is returned invisibly with the following components. 

threshold : The x axis values. 

meanExcess : The y axis values. Each value is a sample mean minus a
          value u. 

_N_o_t_e:

     The function is designed for speed and not accuracy, therefore
     huge data sets with extremely large values may cause failure (the
     function 'cumsum' is used.) Ties may not be well handled.

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

     T. W. Yee

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

     Davison, A. C. and Smith, R. L. (1990) Models for exceedances over
     high thresholds (with discussion). _Journal of the Royal
     Statistical Society, Series B, Methodological_, *52*, 393-442.

     Coles, S. (2001) _An Introduction to Statistical Modeling of
     Extreme Values_. London: Springer-Verlag.

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

     'gpd'.

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

     ## Not run: 
     meplot(runif(500), las=1) -> i
     names(i)
     ## End(Not run)

