# internals_for_qqplot

##### Internal functions for qqplot of package distr

These functions are used internally by qqplot of package distr.

- Keywords
- internal

##### 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

##### 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`

, \(\alpha\), \(\delta\),
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.

`.distrExInstalled`

is a constant logical --- `TRUE`

if package
distrEx is installed.

##### Value

a logical vector of same length as `x`

.

a logical vector of same length as `x`

.

a logical vector of same length as `x`

.

a vector of same length as `x`

with entries in the
set \(\{0,1,2,3,4\}\).

a numeric of length `length(ord`

.

a numeric of length 1: the discrepancy $$P(\sqrt{n} |X-x-\delta| \leq t) - \alpha$$

a numeric matrix with two columns `"left"`

and `"right"`

with the corresponding pointwise confidence widths.

a numeric matrix with two columns `"left"`

and `"right"`

with the corresponding pointwise confidence widths.

a numeric of length 1; a corresponding quantile of the (exact/asymptotic) Kolmogorov distribution

a numeric matrix with two columns `"left"`

and `"right"`

with the corresponding pointwise confidence widths.

`invisible(NULL)`

the manipulated list of arguments

##### See Also

*Documentation reproduced from package distr, version 2.8.0, License: LGPL-3*