# 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`

, $\code{alpha}$, $\code{del}$,
and for $X distributed as D$, the discrepancy
$$P(\sqrt{n} |X-x-\delta| \leq t) - \alpha$$

`.BinomCI`

, in a vectorized form, computes,
for given `x`

, $\code{alpha}$, $\code{del}$,
values `t`

such that,
pointwise in `x`

and for $X distributed as D$,
$$P(\sqrt{n} |X-x-\delta| \leq t) = \alpha$$

`.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

- .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

##### See Also

*Documentation reproduced from package distr, version 2.6, License: LGPL-3*