cdf... (cumulative distribution functions)
and qua... (quantile functions) expect the distribution
parameters to be specified as a single vector.
This differs from the standard Rconvention, in which
each parameter is a separate argument.
There are two reasons for this.
First, the single-vector parameterization is consistent with
the Fortran routines on which these Rfunctions are based.
Second, the single-vector parametrization is often easier to use.
For example, consider computing the 80th and 90th percentiles
of a normal distribution fitted to a set of $L$-moments
stored in a vector lmom.
In the single-vector parametrization, this is achieved by
quanor( c(.8,.9), pelnor(lmom) )
The separate-arguments parametrization would need a more complex
expression, such as
do.call( qnorm, c( list(.8,.9), pelnor(lmom) ) )
In functions (lmrp, lmrq, pelp, pelq, evplot,
evdistp, evdistq) that take a cumulative distribution function
or a quantile function as an argument, the cumulative distribution function
or quantile function can use either form of parametrization.cdf..., qua..., lmr..., pel...,
and samlmu are analogous to Fortran routines from
the LMOMENTS package, version 3.04, available from StatLib at
cdfwak and samlmu, and all the lmr... and pel...
functions, internally call Fortran code that is derived from the
LMOMENTS package.cdf...
computes the cumulative distribution function of the distribution.
qua...
computes the quantile function (inverse cumulative distribution function)
of the distribution.
lmr...
calculates the $L$-moment ratios of the distribution given its
parameters.
pel...
calculates the parameters of the distribution given its $L$-moments.
When the $L$-moments are the sample $L$-moments of a set of data,
the resulting parameters are of course the
... is a three-letter code used to identify the
distribution, as given in the table below.
For example the cumulative distribution function of the gamma distribution is
cdfgam.
exp exponential
gam gamma
gev generalized extreme-value
glo generalized logistic
gpa generalized Pareto
gno generalized normal
gum Gumbel (extreme-value type I)
kap kappa
ln3 lognormal
nor normal
pe3 Pearson type III
wak Wakeby
wei Weibull
}
The following functions are also contained in the package.
samlmu
computes the sample $L$-moments of a data vector.
lmrp and lmrq
compute the $L$-moments of a probability distribution specified
by its cumulative distribution function (for function lmrp)
or its quantile function (for function lmrq).
The computation uses numerical integration applied to
a general expression for the $L$-moments of a distribution.
Functions lmrp and lmrq can be used for any univariate
distribution. They are slower and usually less accurate than the
computations carried out for specific distributions by the
lmr... functions.
pelp and pelq
compute the parameters of a probability distribution
as a function of the $L$-moments.
The computation uses function lmrp or lmrq to compute
$L$-moments and numerical optimization to find parameter values
for which the sample and population $L$-moments are equal.
Functions pelp and pelq can be used for any univariate
distribution. They are slower and usually less accurate than the
computations carried out for specific distributions by the
pel... functions.
lmrd
draws an $L$-moment ratio diagram.
lmrdpoints and lmrdlines
add points, or connected line segments, respectively,
to an $L$-moment ratio diagram.
evplot
draws an evpoints, evdistp, and evdistq
add, respectively, a set of points, a cumulative distribution function,
and a quantile function to an extreme-value plot.