# 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)
.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"))
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 pos
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
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
...
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. .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. .fillList fills a new list with the elements of a given list list0 until length len is reached using recycling 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://article.gmane.org/gmane.comp.lang.r.general/126112. .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. devNew opens a new device. This function is for back compatibility with R versions < 2.8.0.

##### Value

• .is.vector.latticelogical (length 1).
• .is.consistentlogical (length 1).
• .notwithLArglogical (length 1).
• .make.lattice.es.vectoran object of class Lattice.
• .inArgslogical (length 1).
• .isIn, .isEqual,.isEqual01vector of logical.
• .fm,.fM, .fM2a numeric of length 1.
• .plusm,.multman object of class DiscreteDistribution or AbscontDistribution according to argument DClass.
• .getObjNamecharacter.
• .discretizePnumeric --- the probabilities for the grid-values.
• .makeDd,.makePd, .makeQda function with args x, y, yleft, yright.
• .makeD,.makeDNewa function with args x, log = FALSE.
• .makeP,.makePNewa function with args q, lower.tail = TRUE, log.p = FALSE.
• .makeQ,.makeQNewa function with args p, lower.tail = TRUE, log.p = FALSE.
• .isInteger,.isNatural,.isNatural0logical (same length as argument x).
• .mergegaps,.mergegaps2a gaps-matrix, i.e.; a matrix m with two columns, such that t(m), interpreted as vector, is ordered.
• .pmixfunslot p for a mixing distribution, i.e. a function function(q, lower.tail = TRUE, log.p = FALSE), which is the cdf of the distribution.
• .dmixfunslot d for a mixing distribution, i.e. a function function(x, log = FALSE), which is the density of the distribution.
• .qmixfunslot 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.
• .rmixfunslot r for a mixing distribution, i.e. a function function(n) generating r.v.'s according to the distribution.
• .deldmixfuna possibly modified argument mixDistr.
• .loupmixfuna 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.castan object of class "UnivarLebDecDistribution".
• .expm.d,.logm.dan object of class "DiscreteDistribution".
• .expm.c,.logm.can object of class "AbscontDistribution".
• .P2Da density d as function function(x, log = FALSE).
• .P2Qa quantile function q as function function(p, lower.tail = TRUE, log.p = FALSE)
• .D2P, .Q2Pa cdf p as function function(q, lower.tail = TRUE, log.p = FALSE).
• .csimpsuma vector of evaluations of the prime function at the grid points.
• .primefunthe prime function as a function.
• .IssueWarna list with two warnings to be issued each of which may be empty.
• .fillLista list.
• .trunc.up,.trunc.lowa list with elements r,p,d,q (in this order).
• .DistrCollapseupon 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.
• devNewreturns the return value of the device opened, usually invisible NULL.

##### concept

utilities

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
• .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
• devNew
Documentation reproduced from package distr, version 2.3.1, License: LGPL-3

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