DiscreteDistribution
-class is the mother-class of the class LatticeDistribution
.new("DiscreteDistribution", ...)
, but more
easily is the use of the generating function "DiscreteDistribution"
.
This generating function, from version 1.9 on, has been moved to this package from package distrEx.img
"Reals"
: the space of the image of this distribution which has dimension 1
and the name "Real Space" param
"Parameter"
: the parameter of this distribution, having only the
slot name "Parameter of a discrete distribution" r
"function"
: generates random numbersd
"function"
: density/probability functionp
"function"
: cumulative distribution functionq
"function"
: quantile function.withArith
.withSim
.logExact
.lowerExact
Symmetry
"DistributionSymmetry"
;
used internally to avoid unnecessary calculations."UnivariateDistribution"
, directly.
Class "Distribution"
, by class "UnivariateDistribution"
.signature(.Object = "DiscreteDistribution")
: initialize method signature(from = "DiscreteDistribution",
to = "LatticeDistribution")
: coerce method to class "LatticeDistribution"
(checks if support is a lattice)signature(x = "DiscreteDistribution")
: application of a mathematical function, e.g. sin
or tan
to this discrete distribution
abs
: signature(x = "DiscreteDistribution")
: exact image distribution of abs(x)
.
exp
: signature(x = "DiscreteDistribution")
: exact image distribution of exp(x)
.
sign
: signature(x = "DiscreteDistribution")
: exact image distribution of sign(x)
.
sqrt
: signature(x = "DiscreteDistribution")
: exact image distribution of sqrt(x)
.
log
: signature(x = "DiscreteDistribution")
: (with optional further argument base
, defaulting to exp(1)
) exact image distribution of log(x)
.
log10
: signature(x = "DiscreteDistribution")
: exact image distribution of log10(x)
.
gamma
: signature(x = "DiscreteDistribution")
: exact image distribution of gamma(x)
.
lgamma
: signature(x = "DiscreteDistribution")
: exact image distribution of lgamma(x)
.
digamma
: signature(x = "DiscreteDistribution")
: exact image distribution of digamma(x)
.
signature(e1 = "DiscreteDistribution")
: application of `-' to this discrete distributionsignature(e1 = "DiscreteDistribution", e2 = "numeric")
: multiplication of this discrete distribution
by an object of class `numeric'signature(e1 = "DiscreteDistribution", e2 = "numeric")
: division of this discrete distribution
by an object of class `numeric'signature(e1 = "DiscreteDistribution", e2 = "numeric")
: addition of this discrete distribution
to an object of class `numeric'signature(e1 = "DiscreteDistribution", e2 = "numeric")
: subtraction of an object of class `numeric'
from this discrete distribution signature(e1 = "numeric", e2 = "DiscreteDistribution")
: multiplication of this discrete distribution
by an object of class `numeric'signature(e1 = "numeric", e2 = "DiscreteDistribution")
: addition of this discrete distribution
to an object of class `numeric'signature(e1 = "numeric", e2 = "DiscreteDistribution")
: subtraction of this discrete distribution
from an object of class `numeric'signature(e1 = "DiscreteDistribution", e2 = "DiscreteDistribution")
: Convolution of two discrete
distributions. The slots p, d and q are approximated on a common grid.signature(e1 = "DiscreteDistribution", e2 = "DiscreteDistribution")
: Convolution of two discrete
distributions. The slots p, d and q are approximated on a common grid.signature(object = "DiscreteDistribution")
: returns the supportsignature(object = "DiscreteDistribution")
: returns the
left continuous cumulative distribution function, i.e.;
$p.l(t) = P(object < t)$ signature(object = "DiscreteDistribution")
: returns the
right-continuous quantile function, i.e.;
$q.r(s)=sup{t|P(object>=t)<=s}$< dd=""> signature(object = "DiscreteDistribution")
: plots density, cumulative distribution and quantile
function "AffLinDiscreteDistribution"
which has extra slots
a
, b
(both of class "numeric"
), and X0
(of class "DiscreteDistribution"
), to capture the fact
that the object has the same distribution as a * X0 + b
. This is
the class of the return value of methods
signature(e1 = "DiscreteDistribution")
signature(e1 = "DiscreteDistribution", e2 = "numeric")
signature(e1 = "DiscreteDistribution", e2 = "numeric")
signature(e1 = "DiscreteDistribution", e2 = "numeric")
signature(e1 = "DiscreteDistribution", e2 = "numeric")
signature(e1 = "numeric", e2 = "DiscreteDistribution")
signature(e1 = "numeric", e2 = "DiscreteDistribution")
signature(e1 = "numeric", e2 = "DiscreteDistribution")
signature(e1 = "AffLinDiscreteDistribution")
signature(e1 = "AffLinDiscreteDistribution", e2 = "numeric")
signature(e1 = "AffLinDiscreteDistribution", e2 = "numeric")
signature(e1 = "AffLinDiscreteDistribution", e2 = "numeric")
signature(e1 = "AffLinDiscreteDistribution", e2 = "numeric")
signature(e1 = "numeric", e2 = "AffLinDiscreteDistribution")
signature(e1 = "numeric", e2 = "AffLinDiscreteDistribution")
signature(e1 = "numeric", e2 = "AffLinDiscreteDistribution")
"AffLinAbscontDistribution"
,
"AffLinDiscreteDistribution"
, "AffLinUnivarLebDecDistribution"
and called "AffLinDistribution"
which is used for functionals."AbscontDistribution"
,
"DiscreteDistribution"
, or "UnivarLebDecDistribution"
,
there is a class union of these classes called "AcDcLcDistribution"
;
in partiucalar methods for "*"
, "/"
,
"^"
(see operators-methods) and methods
Minimum
, Maximum
, Truncate
, and
Huberize
, and convpow
are defined for this
class union.Parameter-class
UnivariateDistribution-class
LatticeDistribution-class
AbscontDistribution-class
Reals-class
RtoDPQ.d
# Dirac-measure at 0
D1 <- DiscreteDistribution(supp = 0)
support(D1)
# simple discrete distribution
D2 <- DiscreteDistribution(supp = c(1:5), prob = c(0.1, 0.2, 0.3, 0.2, 0.2))
plot(D2)
(pp <- p(D2)(support(D2)))
p(D2)(support(D2)-1e-5)
p(D2)(support(D2)+1e-5)
p.l(D2)(support(D2))
p.l(D2)(support(D2)-1e-5)
p.l(D2)(support(D2)+1e-5)
q(D2)(pp)
q(D2)(pp-1e-5)
q(D2)(pp+1e-5)
q.r(D2)(pp)
q.r(D2)(pp-1e-5)
q.r(D2)(pp+1e-5)
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