DISTPLOTS               package:nsRFA               R Documentation

_E_m_p_i_r_i_c_a_l _d_i_s_t_r_i_b_u_t_i_o_n _p_l_o_t_s

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

     Sample values are plotted against their empirical distribution in
     graphs where points belonging to a particular distribution should
     lie on a straight line.

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

      plotpos (x, a=0, orient="xF", ...)
      plotposRP (x, a=0, orient="xF", ...)
      loglogplot (x, a=0, orient="xF", ...)
      unifplot (x, a=0, orient="xF", line=FALSE, ...)
      normplot (x, a=0, orient="xF", line=FALSE, ...)
      lognormplot (x, a=0, orient="xF", line=FALSE, ...)
      studentplot (x, df, a=0, orient="xF", line=FALSE,...)
      logisplot (x, a=0, orient="xF", line=FALSE,...)
      gammaplot (x, shape, a=0, orient="xF", line=FALSE,...)
      expplot (x, a=0, orient="xF", line=FALSE,...)
      paretoplot (x, a=0, orient="xF", line=FALSE,...)
      gumbelplot (x, a=0, orient="xF", line=FALSE, ...)
      frechetplot (x, a=0, orient="xF", line=FALSE,...)
      weibullplot (x, a=0, orient="xF", line=FALSE,...)
      pointspos (x, a=0, orient="xF", ...)
      pointsposRP (x, a=0, orient="xF", ...)
      loglogpoints (x, a=0, orient="xF", ...)
      unifpoints (x, a=0, orient="xF", ...)
      normpoints (x, a=0, orient="xF", ...)
      studentpoints (x, df, a=0, orient="xF", ...)
      logispoints (x, a=0, orient="xF", ...)
      gammapoints (x, shape, a=0, orient="xF", ...)
      exppoints (x, a=0, orient="xF", ...)
      gumbelpoints (x, a=0, orient="xF", ...)
      weibullpoints (x, a=0, orient="xF", ...)
      regionalplotpos (x, cod, a=0, orient="xF", ...)
      regionalnormplot (x, cod, a=0, orient="xF", ...)
      regionallognormplot (x, cod, a=0, orient="xF", ...)
      regionalexpplot (x, cod, a=0, orient="xF", ...)
      regionalparetoplot (x, cod, a=0, orient="xF", ...)
      regionalgumbelplot (x, cod, a=0, orient="xF", ...)
      regionalfrechetplot (x, cod, a=0, orient="xF", ...)

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

       x: vector representing a data-sample

      df: degrees of freedom (> 0, maybe non-integer) of the Student t
          distribution.  'df = Inf' is allowed.

   shape: shape parameter of the distribution

       a: plotting position parameter, normally between 0 and 0.5 (the
          default value here, corresponding to the Hazen plotting
          position, see details)

  orient: if 'orient="xF"' the abscissa will be x and the ordinate F

    line: if TRUE (default) a straight line indicating the normal,
          lognormal, ..., distribution with parameters estimated from
          'x' is plotted

     cod: array that defines the data subdivision among sites

     ...: graphical parameters as 'xlab', 'ylab', 'main', ...

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

     A brief introduction on Probability Plots (or Quantile-Quantile
     plots) is available on <URL:
     http://en.wikipedia.org/wiki/Q-Q_plot>. For plotting positions see
     <URL: http://en.wikipedia.org/wiki/Plotting_position>.

     For the quantiles of the comparison distribution typically the
     Weibull formula k/(n + 1) is used (default here).  Several
     different formulas have been used or proposed as symmetrical
     plotting positions.  Such formulas have the form 

                         (k - a)/(n + 1 - 2a)

     for some value of a in the range from 0 to 1/2.  The above
     expression k/(n+1) is one example of these, for a=0.  The Filliben
     plotting position has a = 0.3175 and the Cunanne plotting position
     has a = 0.4 should be nearly quantile-unbiased for a range of
     distributions. The Hazen plotting position, widely used by
     engineers, has a = 0.5. The Blom's plotting position, a = 3/8,
     gives nearly unbiased quantiles for the normal distribution, while
     the Gringeton plotting position, a = 0.44, is optimized for the
     largest observations from a Gumbel distribution. For the
     generalized Pareto, the GEV and related distributions of the Type
     I (Gumbel) and Weibull, a = 0.35 is suggested.

     For large sample size, n, there is little difference between these
     various expressions.

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

     Representation of the values of 'x' vs their empirical probability
     function F in a cartesian, uniform, normal, lognormal or Gumbel
     plot.  'plotpos' and 'unifplot' are analogous except for the axis
     notation, 'unifplot' has the same notation as 'normplot',
     'lognormplot', ... 'plotposRP' is analogous to 'plotpos' but the
     frequencies F are expressed as Return Periods T=1/(1-F). With the
     default settings, F is defined with the Weibull plotting position
     F=k/(n+1). The straight line (if 'line'=TRUE) indicate the
     uniform, normal, lognormal or Gumbel distribution with parameters
     estimated from 'x'. The regional plots draw samples of a region on
     the same plot. 

     'pointspos', 'normpoints', ... are the analogous of 'points', they
     can be used to add points or lines to 'plotpos', 'normplot', ...
     'normpoints' can be used either on 'normplot' or 'lognormplot'.
     'exppoints' can be used either on 'expplot' or 'paretoplot' (since
     the log-transformed Pareto random variable is exponentially
     distributed). 'gumbelpoints' can be used either on 'gumbelplot' or
     'frechetplot' (since the log-transformed Frechet random variable
     is distributed as a Gumbel).

     'loglogplot' plots the logarithm of sample vs the logarithm of the
     empirical exceedance probability. For the log-log plot, the tail
     probability is represented by a straight line for power-law
     distributions (e.g. log-pearson, log-logistic, Frechet, ..., HEAVY
     TAIL), but not for the other subexponential or exponential
     distributions (e.g. gumbel, gamma, Pearson type III, ..., MODERATE
     TAIL); see El Adlouni et al. (2008).

_N_o_t_e:

     For information on the package and the Author, and for all the
     references, see 'nsRFA'.

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

     These functons are analogous to 'qqnorm'; for the distributions,
     see 'Normal', 'Lognormal', 'LOGNORM', 'GUMBEL'.

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

     x <- rnorm(30,10,2)
     plotpos(x)
     normplot(x)
     normplot(x,xlab=expression(D[m]),ylab=expression(hat(F)),
              main="Normal plot",cex.main=1,font.main=1)
     normplot(x,line=FALSE)

     x <- rlnorm(30,log(100),log(10))
     normplot(x)
     lognormplot(x)

     x <- rand.gumb(30,1000,100)
     normplot(x)
     gumbelplot(x)

     x <- rnorm(30,10,2)
     y <- rnorm(50,10,3)
     z <- c(x,y)
     codz <- c(rep(1,30),rep(2,50))
     regionalplotpos(z,codz)
     regionalnormplot(z,codz,xlab="z")
     regionallognormplot(z,codz)
     regionalgumbelplot(z,codz)

     plotpos(x)
     pointspos(y,pch=2,col=2)

     x <- rnorm(50,10,2)
     F <- seq(0.01,0.99,by=0.01)
     qq <- qnorm(F,10,2)
     plotpos(x)
     pointspos(qq,type="l")

     normplot(x,line=FALSE)
     normpoints(x,type="l",lty=2,col=3)

     lognormplot(x)
     normpoints(x,type="l",lty=2,col=3)

     gumbelplot(x)
     gumbelpoints(x,type="l",lty=2,col=3)

     # distributions comparison in probabilistic graphs
     x <- rnorm(50,10,2)
     F <- seq(0.001,0.999,by=0.001)
     loglikelhood <- function(param) {-sum(dgamma(x, shape=param[1], 
                     scale=param[2], log=TRUE))}
     parameters <- optim(c(1,1),loglikelhood)$par
     qq <- qgamma(F,shape=parameters[1],scale=parameters[2])
     plotpos(x)
     pointspos(qq,type="l")

     normplot(x,line=FALSE)
     normpoints(qq,type="l")

     lognormplot(x,line=FALSE)
     normpoints(qq,type="l")

