| operators-methods {distr} | R Documentation |
Arithmetics and unary mathematical transformations for distributions
e1,e2 |
objects of class "UnivariateDistribution" (or subclasses) or "numeric" |
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
-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
UnivariateDistribution-class
AbscontDistribution-class
DiscreteDistribution-class
Norm-class
Binom-class
Pois-class
Dirac-class
Cauchy-class
Gammad-class
Exp-class
Nbinom-class
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)