operators-methods {distr}R Documentation

Methods for operators +,-,*,/ in Package distr

Description

Arithmetics and unary mathematical transformations for distributions

Arguments

e1,e2 objects of class "UnivariateDistribution" (or subclasses) or "numeric"

Details

Arithmetics as well as all functions from group Math, see Math are provided for distributions; wherever possible exact expressions are used; else random variables are generated according to this transformation and subsequently the remaining slots filled by RtoDPQ, RtoDPQ.d

Methods

-
signature(e1 = "UnivariateDistribution", e2 = "missing") unary operator; result again of class "UnivariateDistribution"; exact
-
signature(e1 = "Norm", e2 = "missing") unary operator; result again of "Norm"; exact
+
signature(e1 = "UnivariateDistribution", e2 = "numeric") result again of class "UnivariateDistribution"; exact
+
signature(e1 = "AbscontDistribution", e2 = "numeric") result again of class "AbscontDistribution"; exact
+
signature(e1 = "DiscreteDistribution", e2 = "numeric") result again of class "DiscreteDistribution"; exact
+
signature(e1 = "Cauchy", e2 = "numeric") result again of class "Cauchy"; exact
+
signature(e1 = "Dirac", e2 = "numeric") result again of class "Dirac"; exact
+
signature(e1 = "Norm", e2 = "numeric") result again of class "Norm"; exact
+
signature(e1 = "Unif", e2 = "numeric") result again of class "Unif"; exact
+
signature(e1 = "numeric", e2 = "UnivariateDistribution") is translated to signature(e1 = "UnivariateDistribution", e2 = "numeric"); exact
-
signature(e1 = "UnivariateDistribution", e2= "ANY");exact
-
signature(e1 = "UnivariateDistribution", e2 = "numeric") is translated to e1 + (-e2); exact
-
signature(e1 = "numeric", e2 = "UnivariateDistribution") is translated to (-e1) + e2; exact
*
signature(e1 = "UnivariateDistribution", e2 = "numeric") result again of class "UnivariateDistribution"; exact
*
signature(e1 = "DiscreteDistribution", e2 = "numeric") result again of class "DiscreteDistribution"; exact
*
signature(e1 = "AbscontDistribution", e2 = "numeric") result again of class "AbscontDistribution"; exact
*
signature(e1 = "Exp", e2 = "numeric") if e2>0 result again of class "Exp"; exact
*
signature(e1 = "ExpOrGammaOrChisq", e2 = "numeric") if e1 is a Gamma distribution and e2>0 result of class "Gammad"; exact
*
signature(e1 = "Cauchy", e2 = "numeric") result again of class "Cauchy"; exact
*
signature(e1 = "Dirac", e2 = "numeric") result again of class "Dirac"; exact
*
signature(e1 = "Norm", e2 = "numeric") result again of class "Norm"; exact
*
signature(e1 = "Unif", e2 = "numeric") result again of class "Unif"; exact
*
signature(e1 = "numeric", e2 = "UnivariateDistribution") is translated to signature(e1 = "UnivariateDistribution", e2 = "numeric"); exact
/
signature(e1 = "UnivariateDistribution", e2 = "numeric") is translated to e1 * (1/e2); exact
+
signature(e1 = "UnivariateDistribution", e2 = "UnivariateDistribution") result again of class "UnivariateDistribution"; is generated by simulations
-
signature(e1 = "UnivariateDistribution", e2 = "UnivariateDistribution") is translated to (-e1) + (-e2); result again of class "UnivariateDistribution"; is generated by simulations
+
signature(e1 = "AbscontDistribution", e2 = "AbscontDistribution") assumes e1, e2 independent; result again of class "AbscontDistribution"; is generated by FFT
+
signature(e1 = "AbscontDistribution", e2 = "DiscreteDistribution") assumes e1, e2 independent; result again of class "AbscontDistribution"; is generated by FFT
+
signature(e1 = "DiscreteDistribution", e2 = "AbscontDistribution") assumes e1, e2 independent; result again of class "AbscontDistribution"; is generated by FFT
+
signature(e1 = "DiscreteDistribution", e2 = "DiscreteDistribution") assumes e1, e2 independent; result again of class "AbscontDistribution"; is generated by explicite convolution
+
signature(e1 = "Binom", e2 = "Binom") assumes e1, e2 independent; if prob(e1)==prob(e2), result again of class "Binom"; uses the convolution formula for binomial distributions; exact
+
signature(e1 = "Chisq", e2 = "Chisq") assumes e1, e2 independent; result again of class "Chisq"; uses the convolution formula for Chisq distributions; exact
+
signature(e1 = "Dirac", e2 = "Dirac") result again of class "Dirac"; exact
+
signature(e1 = "ExpOrGammaOrChisq", e2 = "ExpOrGammaOrChisq") assumes e1, e2 independent; if e1, e2 are Gamma distributions, result is of class "Gammad"; uses the convolution formula for Gamma distributions; exact
+
signature(e1 = "Pois", e2 = "Pois") assumes e1, e2 independent; result again of class "Pois"; uses the convolution formula for Poisson distributions; exact
+
signature(e1 = "Nbinom", e2 = "Nbinom") assumes e1, e2 independent; if prob(e1)==prob(e2), result again of class "Nbinom"; uses the convolution formula for negative binomial distributions; exact
+
signature(e1 = "Norm", e2 = "Norm") assumes e1, e2 independent; result again of class "Norm"; uses the convolution formula for normal distributions; exact
+
signature(e1 = "UnivariateDistribution", e2 = "Dirac") translated to e1 + location(e2); result again of class "Dirac"; exact
+
signature(e1 = "Dirac", e2 = "UnivariateDistribution") translated to e2 + location(e1); result again of class "Dirac"; exact
-
signature(e1 = "Dirac", e2 = "Dirac") result again of class "Dirac"; exact
*
signature(e1 = "Dirac", e2 = "Dirac") result again of class "Dirac"; exact
*
signature(e1 = "UnivariateDistribution", e2 = "Dirac") translated to e1 * location(e2); result again of class "Dirac"; exact
*
signature(e1 = "Dirac", e2 = "UnivariateDistribution") translated to e2 * location(e1); result again of class "Dirac"; exact
/
signature(e1 = "Dirac", e2 = "Dirac") result again of class "Dirac"; exact

See Also

UnivariateDistribution-class AbscontDistribution-class
DiscreteDistribution-class Norm-class Binom-class Pois-class
Dirac-class Cauchy-class Gammad-class Exp-class Nbinom-class

Examples

N <- Norm(0,3)
P <- Pois(4)
a <- 3
N + a
N + P
N - a
a * N
a * P
N / a + sin( a * P - N)

[Package distr version 1.7 Index]