internals_for_qqplot: Internal functions for qqplot of package distr

Description

These functions are used internally by qqplot of package distr.

Usage

.inGaps(x,gapm)
.isReplicated(x, tol = .Machine$double.eps)
.NotInSupport(x,D)
.SingleDiscrete(x,D)
.makeLenAndOrder(x,ord)
.BinomCI.in(t,p.bi,x.i, del.i=0,D.i,n.i,alpha.i)
.BinomCI(x,p.b,D,n,alpha, silent0 = TRUE)
.BinomCI.nosym(x,p.b,D,n,alpha, silent0 = TRUE)
.q2kolmogorov(alpha,n,exact=(n<100), silent0="TRUE)" .q2pw(x,p.b,d,n,alpha,exact="(n<100),nosym=FALSE,">
.confqq(x,D, datax=FALSE, withConf.pw  = TRUE,  withConf.sim = TRUE, alpha,
                    col.pCI, lty.pCI, lwd.pCI, pch.pCI, cex.pCI,
                    col.sCI, lty.sCI, lwd.sCI, pch.sCI, cex.sCI,
                    n,exact.sCI=(n<100),exact.pci=(n<100), nosym.pci="FALSE," with.legend="TRUE," legend.bg="white" ,="" legend.pos="topleft" legend.cex="0.8," legend.pref="" legend.postf="" legend.alpha="alpha," qqb0="NULL," transf0="NULL," debug="FALSE)
.deleteItemsMCL(mcl)
.distrExInstalled

Value

.inGaps: a logical vector of same length as x.
.isReplicated: a logical vector of same length as x.
.NotInSupport: a logical vector of same length as x.
.SingleDiscrete: a vector of same length as x with entries in the set $\{0,1,2,3,4\}$.
.makeLenAndOrder: a numeric of length length(ord.
.BinomCI.in: a numeric of length 1: the discrepancy $$P(\sqrt{n} |X-x-\delta| \leq t) - \alpha$$
.BinomCI: a numeric matrix with two columns "left" and "right" with the corresponding pointwise confidence widths.
.BinomCI.nosym: a numeric matrix with two columns "left" and "right" with the corresponding pointwise confidence widths.
.q2kolmogorov: a numeric of length 1; a corresponding quantile of the (exact/asymptotic) Kolmogorov distribution
.q2pw: a numeric matrix with two columns "left" and "right" with the corresponding pointwise confidence widths.
.confqq: invisible(NULL)
.deleteItemsMCL: the manipulated list of arguments

Arguments

x: a (numeric) vector
gapm: matrix; the gap matrix as in slot gaps of an "AbscontDistribution" or "UnivarLebDecDistribution" object.
tol: numeric; tolerance for separating points.
D: object of class "UnivariateDistribution"
datax: logical; (to be used in distrMod) shall data be plotted on x-axis?
ord: integer; the result of a call to order
alpha: numeric in [0,1]; confidence level
n: integer; sample size
exact: logical; shall finite sample version be used?
t: current (half of the) width of the confidence interval.
p.bi: (local) (binomial) c.d.f. value at x.i.
x.i: a (numeric) vector
del.i: numeric; a (local) asymmetry parameter to pass on to optim and uniroot --- the endpoints of the searched interval are x.i+t/sqrt(n)+del.i/sqrt(n) and x.i-t/sqrt(n)+del.i/sqrt(n).
D.i: object of class "UnivariateDistribution"
n.i: integer; (local) sample size
alpha.i: numeric in [0,1]; (local) confidence level
p.b: (binomial) c.d.f. value at x.
nosym: logical; shall we compute shortest (asymmetric) confidence intervals;
withConf.pw: logical; shall pointwise confidence lines be plotted?
withConf.sim: logical; shall simultaneous confidence lines be plotted?
exact.pCI: logical; shall pointwise CIs be determined with exact Binomial distribution?
exact.sCI: logical; shall simultaneous CIs be determined with exact kolmogorov distribution?
nosym.pCI: logical; shall we use (shortest) asymmetric CIs?
col.pCI: color for the pointwise CI
lty.pCI: line type for the pointwise CI
lwd.pCI: line width for the pointwise CI
pch.pCI: symbol for points (for discrete mass points) in pointwise CI
cex.pCI: magnification factor for points (for discrete mass points) in pointwise CI
col.sCI: color for the simultaneous CI
lty.sCI: line type for the simultaneous CI
lwd.sCI: line width for the simultaneous CI
pch.sCI: symbol for points (for discrete mass points) in simultaneous CI
cex.sCI: magnification factor for points (for discrete mass points) in simultaneous CI
with.legend: logical; shall a legend be plotted?
legend.bg: background color for the legend
legend.pos: position for the legend
legend.cex: magnification factor for the legend
legend.pref: character to be prepended to legend text
legend.postf: character to be appended to legend text
legend.alpha: nominal coverage probability
mcl: arguments in call as a list
qqb0: precomputed return value of qqbounds
transf0: optional transformation of x-values (by default NULL and then ignored)
debug: logical; if TRUE additional output to debug confidence bounds.
silent0: logical; it is used as argument silent in try-catches within this function.

Author

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,

Details

.inGaps produces a logical vector of same length as x with entries TRUE if the corresponding component of x lies within a gap as given by gap matrix gapm and FALSE otherwise.

.isReplicated produces a logical vector of same length as x with entries TRUE if the corresponding component of x appears at least twice within x and FALSE otherwise.

.NotInSupport produces a logical vector of same length as x with entries TRUE if the corresponding component of x does not lie within the support of D and FALSE otherwise.

.SingleDiscrete produces a numerical vector of same length as x with values 0 if the corresponding component of x is discrete mass point of D, 1 if the corresponding component of x lies within the continuous support of D, 2 and 3 if the corresponding component of x is a left resp. right end point of a gap of D, and 4 if the corresponding component of x does not lie within the support of D at all.

.makeLenAndOrder by standard recycling roules respectively by truncation at the end, forces x to length length{ord} and then orders the result according to ord.

.q2kolmogorov, in the finite sample version (exact==TRUE), returns the corresponding alpha-quantile of the exact Kolmogorov distribution multiplied by $\sqrt{n}$, and in the asymptotic version (exact==FALSE), the the corresponding (upper) alpha-quantile of the asymptotic Kolmogorov distribution. Doing so we make use of C-function "pkolmogorov2x" (from ks.test in package stats) and R-function pkstwo (again from ks.test in package stats).

.BinomCI.in in a non-vectorized form, computes, for given t, x, $\alpha$, $\delta$, and for $X\sim D$, the discrepancy $$P(\sqrt{n} |X-x-\delta| \leq t) - \alpha$$

.BinomCI, in a vectorized form, computes, for given x, $\alpha$, $\delta$, values t such that, pointwise in x and for $X\sim D$, $$P(\sqrt{n} |X-x-\delta| \leq t) = \alpha$$

.BinomCI.nosym, in an outer loop, by varying del in the former formula, tries to minimize the length of a corresponding level alpha confidence interval containing the estimate.

.q2pw computes pointwise finite sample or asymptotic confidence widths by means of binomial probabilities / quantiles, in the former case either symmetric (default) or shortest asymmetric; in the asymptotic case, for distributions without a Lebesgue density, for the corresponding density value at the quantile appearing in the expression for the asymptotic variance, we make an approximation of (D-E(D))/sd(D) by the standard normal, using the density of the latter one; this latter approximation is only available if .distrExInstalled == TRUE; otherwise the corresponding columns will be filled with NA.

.confqq calls qqbound to compute the confidence intervals and plots them; returns the return value of qqbound.

.deleteItemsMCL deletes arguments from a call list which functions like plot, lines, points cannot digest; this is necessary in the manipulation of an original call to a specific qqplot method to pass on the ... argument correctly to calls the mentioned functions.