# internals_for_distr

0th

Percentile

##### Internal functions of package distr

These functions are used internally by package distr.

Keywords
internal
##### Usage
.is.vector.lattice(x)
.is.consistent(lattice, support, eq.space = TRUE)
.make.lattice.es.vector(x)
.inArgs(arg, fct)
.isEqual(p0, p1, tol = min( getdistrOption("TruncQuantile")/2,
.Machine$double.eps^.7)) .isEqual01(x) .isIn(p0, pmat, tol = min( getdistrOption("TruncQuantile")/2, .Machine$double.eps^.7
))
.isInteger(x, tol = .Machine$double.eps) .isNatural(x, tol = .Machine$double.eps)
.isNatural0(x, tol = .Machine$double.eps) .setEqual(x, y, tol = 1e-7) .presubs(inp, frompat, topat) .makeD(object, argList, stand = NULL, fac = NULL) .makeP(object, argList, sign = TRUE, correct = NULL, fac = NULL, fac2 = NULL) .makeQ(object, lastCall, sign = TRUE, Cont = TRUE) .plusm(e1, e2, Dclass = "DiscreteDistribution") .multm(e1, e2, Dclass = "DiscreteDistribution") .notwithLArg(D) .getObjName(i = 1) .discretizeP(D, lower, upper, h) .fm(x,f) .fM(x,f) .fM2(x,f) .makeDd(x,y, yleft, yright) .makePd(x,y, yleft, yright) .makeQd(x,y, yleft, yright) .makeQc(x,y, yleft, yright) .makeDNew(x, dx, h = NULL, Cont = TRUE, standM = "sum") .makePNew(x, dx, h = NULL, notwithLLarg = FALSE, Cont = TRUE, myPf = NULL, pxl = NULL, pxu = NULL) .makeQNew(x, px.l, px.u, notwithLLarg = FALSE, yL , yR, Cont = TRUE) .mergegaps(gaps, support) .mergegaps2(gaps1, gaps2) .consolidategaps(gaps) .pmixfun(mixDistr, mixCoeff, leftright = "right") .dmixfun(mixDistr, mixCoeff, withStand = FALSE, supp = NULL) .rmixfun(mixDistr, mixCoeff) .qmixfun(mixDistr, mixCoeff, Cont = TRUE, pnew, gaps = NULL, leftright = "left") .del0dmixfun(mixDistr) .loupmixfun(mixDistr) .ULC.cast(x) .expm.d(e1) .expm.c(e1) .logm.d(e1) .logm.c(e1) .P2D (p, xx, ql, qu, ngrid = getdistrOption("DefaultNrGridPoints")) .P2Q (p, xx, ql,qu, ngrid = getdistrOption("DefaultNrGridPoints"), qL = -Inf, qU = Inf) .D2P (d, xx, ql, qu, ngrid = getdistrOption("DefaultNrGridPoints")) .Q2P (q, ngrid = getdistrOption("DefaultNrGridPoints")) .csimpsum(fx) .primefun(f,x, nm = NULL) .IssueWarn(Arith,Sim) .List(list0) .fillList(list0, len=length(list0)) .trunc.up(object, upper) .trunc.low(object, lower) .modifyqgaps(pfun, qfun, gaps, leftright = "left") .DistrCollapse(support, prob, eps = getdistrOption("DistrResolution")) .EuclidAlgo(n1,n2) .getCommonWidth(x1,x2, tol=.Machine$double.eps)
.convDiscrDiscr(e1,e2)
.inWithTol(x,y,tol=.Machine\$double.eps)
.panel.mingle(dots,element)
devNew(...)
##### Arguments
x

a (numeric) vector, or (in case of .ULC.cast) an object of class "AcDcLcDistribution"

y

a (numeric) vector

f

a function in one (numeric) argument

lattice

a lattice (of class Lattice)

support

a support vector

eq.space

logical: shall we check for the support to be equally spaced?

arg

a formal argument as character

fct

a function

p0,p1

(numeric) vectors

pmat

(matrix) a matrix with two columns where row-wise the left column is smaller than the right one

tol

an error tolerance (numeric)

e1

a distribution object

e2

a numeric

object

a distribution object

argList

an (unevaluated) list of arguments passed to m(object) where m is in d,p,q

stand

factor for a (Lebesgue) density to integrate to 1

sign

the sign of the second operand --- for multiplication at the moment

correct

unevaluated R-code to correct for right-continuity (for multiplication with negative numerics at the moment)

fac

factor to be multiplied with the return value

fac2

factor to be added to the return value

lastCall

unevaluated R-Code ---gives how the result of a call to q(e1) is further transformed

Cont

logical: TRUE if object is continuous

DClass

character: name of distribution class

D

a distribution object

i

an integer

yleft, yright

extrapolation value beyond left/right endpoint of grid

h

numeric: grid width

standM

standardization method --- summation or integration

notwithLLarg

logical --- can we use log.p, lower.tail arguments for p,q-methods of first operand?

dx

numeric: vector of cell-probabilities for the (discretized) distribution

myPf

function with args x,y, yleft, yright (as approxfun): if given: replaces approxfun as interpolation method for continuos distributions

pxl,pxu

numeric: if given vector of (lower/upper) cumulative probabilities

yL, yR

argmin / argmax of p()-method

inp

either a language object or a character vector

frompat

vector of character strings containing regular expressions (or character string for fixed = TRUE) to be matched in the given character vector. Coerced by as.character to a character string if possible; (as argument pattern in gsub --- but possibly of length >1).

topat

a (vector of) replacement(s) for matched pattern in .presubs. Coerced to character if possible. For fixed = FALSE this can include backreferences "\1" to "\9" to parenthesized subexpressions of pattern. For perl = TRUE only, it can also contain "\U" or "\L" to convert the rest of the replacement to upper or lower case; (as argument replacement in gsub--- but possibly of length >1).

gaps,gaps1,gaps2

matrices m with two columns, such that t(m), interpreted as vector, is ordered

support

support vector of a univariate discrete distribution

prob

probability vector for a univariate discrete distribution

mixDistr

an object of class UnivarDistrList

mixCoeff

an object of class numeric; a probability vector

pnew

a function function(q, lower.tail = TRUE, log.p = FALSE realizing slot p in a distribution object.

withStand

logical; if TRUE a standardization is made such that the sum of the values of the result evaluated at argument supp is 1

supp

NULL or numeric; if withStand is TRUE used to standardize such that the result is a probability density.

p,pfun

slot p of an object of class "AbscontDistribution"

d

slot d of an object of class "AbscontDistribution"

q,qfun

slot q of an object of class "AbscontDistribution"

xx

a given grid of x-values for functions p, d to be evaluated at

ql,qu

lower and upper getdistrOption("TruncQuantile")-quantile of the distribution; also, if argument xx is missing, left and right endpoint of a regular grid of ngrid gridpoints to be used in place of xx.

qL,qU

argmin / argmax of p()-method

ngrid

number of gridpoints

fx

a vector of function evaluations multiplied by the gridwidth

f

a vector of function evaluations

nm

an optional right asymptotic value

Arith

logical; slot .withArith of a distribution object, or logically-any'' of these slots in a collection of such objects

Sim

logical; slot .withSim of a distribution object, or logically-any'' of these slots in a collection of such objects

list0

list, the elements of which are to be copied to a new list using recycling if necessary

len

length of the list to be filled

lower

lower truncation point

upper

upper truncation point

leftright

character; for slot q: if partially matched to "right" function will return the right continuous version, else the left continuous version; for slot p: if partially matched to "left" the left continuous version, else the right continuous version;

n1

integer argument for .EuclidAlgo

n2

integer argument for .EuclidAlgo

x1

width argument for .getCommonWidth

x2

width argument for .getCommonWidth

dots

the unevaluated … argument

element

the name of the item in the unevaluated … argument

...

arguments passed through to other functions

##### Details

.is.vector.lattice checks whether a given vector x is equally spaced. .is.consistent checks whether a given support vector support is consistent to a given lattice lattice --- with or without checking if support is equally spaced. .make.lattice.es.vector makes an object of class Lattice out of a given (equally spaced) vector x.

.inArgs checks whether an argument arg is a formal argument of fct --- not vectorized.

.isEqual checks whether p0 and p1 are equal to given tolerance. .isIn checks whether p0 lies in any of the intervals given by matrix pmat to given tolerance. .isEqual01(x) checks whether x is 0 or 1 to given tolerance. .setEqual sets all elements of x which are equal to some element of y up to tolerance tol, to exactly the respective element of y.

.notwithLArg checks whether object D was generated by simulations or if its slots p,q do not have lower.tail arguments.

.getObjName returns the name of the object in the ith operand. .discretizeP discretizes D to a grid of probabilities from lower to upper with width h.

.fm, .fM return the smallest / biggest value in (0,1) such that f(x) is finite; .fM2 is a variant of .fM using a lower.tail = FALSE argument.

.makeD, .makeP, .makeQ generate slots p,d,q for binary operations e1 /op/ e2 for a distribution object e1 and a numeric e2 ---for the moment only /op/'s +,-,*,/ are implemented.

.plusm, .multm more specifically use .makeD, .makeP, .makeQ to generate slots p,d,q for +, *, respectively.

.makeDd, .makePd, .makeQd provide discrete analogues to approxfun for interpolation at non grid-values

.makeQc is an analogue to makeQd for absolutely continuous distributions using approxfun.

.makeDNew generates slot d for a new distribution object. In case of a discrete distribution it produces a step function with stepfun (using .makeDd) and standardizes to 1 by summation. In case of a continuous distribution it produces a density function with approxfun and standardizes to 1 by integration if the latter fails, it uses a trapezoid rule / summation for this purpose.

.makePNew generates slot p for a new distribution object. In case of a discrete distribution it produces a step function from cumsum applied to dx ---or from pxl if this is given, with stepfun (using .makePd). In case of a continuous distribution it produces a cdf with approxfun. In case of RtoDPQ, approxfun is replaced by myPf which calls ecdf directly.

.makeQNew generates slot q for a new distribution object. In case of a discrete distribution it produces a step function (using .makeQd). Special care is taken for left continuity... In case of a continuous distribution it produces a quantile function with approxfun.

.isInteger, .isNatural, and .isNatural0 test for each coordinate of argument x whether it is integer [natural / natural or 0] or not.

.mergegaps modifies the gaps matrix of an a.c. distribution according to the support slot of a discrete distribution; if necessary, a gap interval [a,b] is split into [a,c],[c,b] if a<c<b. .mergegaps2 merges two gap matrices of two a.c. distributions X1 and X2 such that in the intervals of the resulting gap matrix, neither X1 nor X2 carries mass. .consolidategaps consolidates a gap matrix, i.e. joins adjacent gap intervals.

.pmixfun, .dmixfun, .rmixfun, and .qmixfun fill the slots p, d, r, and q of a corresponding mixing distribution according to the arguments in mixDistr, mixCoeff.

.loupmixfun finds commun lower and upper bounds for the support of the mixing distribution.

.del0dmixfun sets (if slot d.ac is not NULL) the return value of slot function d.ac of mixDistr for argument 0 to 0.

.ULC.cast coerces an object of class "AcDcLcDistribution" to class "UnivarLebDecDistribution", using simplifyD.

.expm.d,.expm.c for discrete, resp. a.c. argument e1 fill the slots p, d, r, and q of the transformation exp(e1) exactly. .logm.d,.logm.c for discrete, resp. a.c. argument e1 fill the slots p, d, r, and q of the transformation log(e1) exactly.

For objects of class AbscontDistribution, .P2D and .P2Q reconstruct function slots d resp. q from function slot p by means of function D1ss from package sfsmisc; and of function .makeQNew, respectively. The other way round, .D2P and .Q2P reconstruct function slot p from from function slots d resp. q by means of function .makePNew and explicite numeric inversion, respectively.

.csimpsum is used internally in .makePNew to produce a primitive function out of function evaluations by means of vectorized Simpson quadrature method, returning already the function values of the prime function on a grid; it is to mimick the behaviour of cumsum. .primefun is similar but more flexible and produces the prime function as a function.

.List checks if argument already is a list, and if so leaves it as it is, otherwise casts it to a list by a call to list.

.fillList fills a new list with the elements of a given list list0 until length len is reached using recycling if necessary. Argument list0 is cast to list by a call to .List if necessary.

.trunc.up, .trunc.low provide common routines for classes DiscreteDistribution and AbscontDistribution for one-sided truncation, using (for slot r) Peter Dalgaard's clever log-tricks as indicated in http://r.789695.n4.nabble.com/help-on-sampling-from-the-truncated-normal-gamma-distribution-on-the-far-end-probability-is-very-low-td868119.html#a868120.

.modifyqgaps modifies slot q for objects of class AbscontDistribution in the presence of gaps, i.e.; if slot gaps is not NULL. If argument leftright does not partially match "right" (default) returns the left continuous version of the quantile function, else the right continuous one.

.EuclidAlgo computes the greatest common divisor of two integers by means of the Euclidean algorithm. .getCommonWidth for two lattices with widths x1 and x2 computes the smallest common lattice width for convolution. .convDiscrDiscr computes the convolution of two discrete distributions by brute force. .inWithTol works like %in% but with a given tolerance.

.panel.mingle is used for mingling arguments panel.first, panel.last in a plot; it returns the evaluated argument element within dots, if it is a symbol; else if it can be interpreted as a call, and if the top call is list, it returns a list of the items of the call to list, unevaluated, and otherwise the unchanged argument.

devNew opens a new device. This function is for back compatibility with R versions < 2.8.0.

##### Value

.is.vector.lattice

logical (length 1).

.is.consistent

logical (length 1).

.notwithLArg

logical (length 1).

.make.lattice.es.vector

an object of class Lattice.

.inArgs

logical (length 1).

.isIn, .isEqual,.isEqual01

vector of logical.

.fm,.fM, .fM2

a numeric of length 1.

.plusm,.multm

an object of class DiscreteDistribution or AbscontDistribution according to argument DClass.

.getObjName

character.

.discretizeP

numeric --- the probabilities for the grid-values.

.makeDd,.makePd, .makeQd

a function with args x, y, yleft, yright.

.makeD,.makeDNew

a function with args x, log = FALSE.

.makeP,.makePNew

a function with args q, lower.tail = TRUE, log.p = FALSE.

.makeQ,.makeQNew

a function with args p, lower.tail = TRUE, log.p = FALSE.

.isInteger,.isNatural,.isNatural0

logical (same length as argument x).

.mergegaps,.mergegaps2

a gaps-matrix, i.e.; a matrix m with two columns, such that t(m), interpreted as vector, is ordered.

.pmixfun

slot p for a mixing distribution, i.e. a function function(q, lower.tail = TRUE, log.p = FALSE), which is the cdf of the distribution.

.dmixfun

slot d for a mixing distribution, i.e. a function function(x, log = FALSE), which is the density of the distribution.

.qmixfun

slot q for a mixing distribution, i.e. a function function(p, lower.tail = TRUE, log.p = FALSE), which is the quantile function of the distribution.

.rmixfun

slot r for a mixing distribution, i.e. a function function(n) generating r.v.'s according to the distribution.

.deldmixfun

a possibly modified argument mixDistr.

.loupmixfun

a list of four components: qL, the minimal value of q(x)(0), ql, the minimal value of q(x)(getdistrOption("TruncQuantile")), qU, the maximal value of q(x)(1), qu, the maximal value of q(x)(getdistrOption("TruncQuantile"), lower.tail = FALSE), x running through the members of mixDistr in each case.

.ULC.cast

an object of class "UnivarLebDecDistribution".

.expm.d,.logm.d

an object of class "DiscreteDistribution".

.expm.c,.logm.c

an object of class "AbscontDistribution".

.P2D

a density d as function function(x, log = FALSE).

.P2Q

a quantile function q as function function(p, lower.tail = TRUE, log.p = FALSE)

.D2P, .Q2P

a cdf p as function function(q, lower.tail = TRUE, log.p = FALSE).

.csimpsum

a vector of evaluations of the prime function at the grid points.

.primefun

the prime function as a function.

.IssueWarn

a list with two warnings to be issued each of which may be empty.

.List

a list.

.fillList

a list.

.trunc.up,.trunc.low

a list with elements r,p,d,q (in this order).

.DistrCollapse

upon a suggestion by Jacob van Etten, jacobvanetten@yahoo.com: help function to collapse the support points of a discrete distributions if they are too close to each other; here argument support is the (original; already sorted) support and prob a corresponding probability vector of same length. Criterium for collapsing: a distance smaller than argument eps.

.EuclidAlgo

returns the greatest common divisor (an integer).

.getCommonWidth

returns the smallest common lattice width (a numeric).

.convDiscrDiscr

returns the convolution of two discrete distributions.

.inWithTol

returns a logical vector of same lenght as x for the matches (up to tolerance) with vector y.

.panel.mingle

used for mingling arguments panel.first, panel.last; returns the evaluated argument element within dots, if it is a symbol; else if it can be interpreted as a call, and if the top call is list, it returns a list of the items of the call to list, unevaluated, and otherwise the unchanged argument.

devNew

returns the return value of the device opened, usually invisible NULL.

AbscontDistribution, DiscreteDistribution, LatticeDistribution, RtoDPQ, RtoDPQ.d, convpow, operators, plot-methods dev.new

##### Aliases
• internals_for_distr
• .is.vector.lattice
• .is.consistent
• .isInteger
• .isNatural
• .isNatural0
• .mergegaps
• .mergegaps2
• .pmixfun
• .dmixfun
• .qmixfun
• .rmixfun
• .del0dmixfun
• .ULC.cast
• .loupmixfun
• .make.lattice.es.vector
• .presubs
• .inArgs
• .EuclidAlgo
• .getCommonWidth
• .isEqual
• .isIn
• .setEqual
• .isEqual01
• .makeD
• .makeP
• .makeQ
• .makeDNew
• .makePNew
• .makeQNew
• .makeDd
• .makePd
• .makeQd
• .makeQc
• .fM2
• .fM
• .fm
• .notwithLArg
• .multm
• .plusm
• .getObjName
• .discretizeP
• .expm.d
• .expm.c
• .logm.d
• .logm.c
• .P2D
• .P2Q
• .D2P
• .Q2P
• .csimpsum
• .primefun
• .IssueWarn
• .fillList
• .trunc.up
• .trunc.low
• .modifyqgaps
• .DistrCollapse
• .convDiscrDiscr
• .inWithTol
• .panel.mingle
• devNew
Documentation reproduced from package distr, version 2.7.0, License: LGPL-3

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