R: Internal functions for qqplot of package distr

internals_for_qqplot {distr} | R Documentation

## 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,

### See Also

`ks.test`, `qqplot` , `qqplot`, `qqplot`

[Package distr version 2.8.0 Index]