# 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)
.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)
.BinomCI.nosym(x,p.b,D,n,alpha)
.q2kolmogorov(alpha,n,exact=(n
```

##### Arguments

- x
- a (numeric) vector
- gapm
- matrix; the gap matrix as in slot
`gaps`

of an`"AbscontDistribution"`

or`"UnivarLebDecDistribution"`

object. - D
- object of class
`"UnivariateDistribution"`

- 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

##### 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 `pkstwo`

(again from `ks.test`

in package `.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.
`.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

##### 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

##### concept

utilities

##### See Also

*Documentation reproduced from package distr, version 2.3.1, License: LGPL-3*