internals-qqplot: Internal functions for qqplot of package distr

Description Usage Arguments Details Value Author(s) See Also

Description

These functions are used internally by qqplot of package distr.

Usage

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.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 [email protected],

See Also

ks.test, qqplot , qqplot, qqplot


distr documentation built on July 9, 2018, 3 a.m.