DISTPLOTS {nsRFA} | R Documentation |
Sample values are plotted against their empirical distribution in graphs where points belonging to a particular distribution should lie on a straight line.
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,...) plotposRPhist (xcont, xhist=NA, infhist=NA, suphist=NA, nbans=NA, seuil=NA, col12=c(1,1), a=0, orient="xF", ...) 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", ...) pointsposRPhist (xcont, xhist=NA, infhist=NA, suphist=NA, nbans=NA, seuil=NA, col12=c(1,1), a=0, orient="xF", ...)
x |
vector representing a data-sample |
xcont |
vector of systematic data (see |
xhist |
vector of historical data (see |
infhist |
inferior limit for historical data (see |
suphist |
superior limit for historical data (see |
nbans |
period (in years) over which the threshold has not been exceeded except for the historical data (see |
seuil |
threshold non exceeded in the historical period except for the historical data (see |
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 |
line |
if TRUE (default) a straight line indicating the normal, lognormal, ..., distribution with parameters estimated from |
cod |
array that defines the data subdivision among sites |
col12 |
vector of 2 elements containing the colors for the systematic and historical data respectively |
... |
graphical parameters as |
A brief introduction on Probability Plots (or Quantile-Quantile plots) is available on http://en.wikipedia.org/wiki/Q-Q_plot. For plotting positions see 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.
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).
plotposRPhist
is based on the method in Stedinger et al. (1993, pp. 18.41-42).
For information on the package and the Author, and for all the references, see nsRFA
.
These functons are analogous to qqnorm
; for the distributions, see Normal
, Lognormal
, LOGNORM
, GUMBEL
.
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")