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distr

internals-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, silent0 = TRUE)

.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

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.

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, \code{alpha}, \code{del}, and for X distributed as D, the discrepancy

P(sqrt(n) abs(X-x-del) <= t) - alpha

.BinomCI, in a vectorized form, computes, for given x, \code{alpha}, \code{del}, values t such that, pointwise in x and for X distributed as D,

P(sqrt(n) abs(X-x-del) <= 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.

.distrExInstalled is a constant logical — TRUE if package distrEx is installed.

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) abs(X-x-del) <= 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

Author(s)

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