# operators-methods

0th

Percentile

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

Arithmetics and unary mathematical transformations for distributions

Keywords
distribution, arith, math
##### 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 of class "AffLinAbscontDistribution"; exact

+

signature(e1 = "DiscreteDistribution", e2 = "numeric") result of class "AffLinDiscreteDistribution"; exact

+

signature(e1 = "LatticeDistribution", e2 = "numeric") result of class "AffLinLatticeDistribution"; exact

+

signature(e1 = "UnivarLebDecDistribution", e2 = "numeric") result of class "AffLinUnivarLebDecDistribution"; exact

+

signature(e1 = "CompoundDistribution", e2 = "numeric") result of class "AffLinUnivarLebDecDistribution"; exact

+

signature(e1 = "AffLinAbscontDistribution", e2 = "numeric") result again of class "AffLinAbscontDistribution"; exact

+

signature(e1 = "AffLinDiscreteDistribution", e2 = "numeric") result again of class "AffLinDiscreteDistribution"; exact

+

signature(e1 = "AffLinLatticeDistribution", e2 = "numeric") result again of class "AffLinLatticeDistribution"; exact

+

signature(e1 = "AffLinUnivarLebDecDistribution", e2 = "numeric") result of class "AffLinUnivarLebDecDistribution"; 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 = "Logis", e2 = "numeric") result again of class "Logis"; 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 = "numeric", e2 = "Beta") if ncp(e2)==0 and e1 == 1, an exact (central) Beta(shape1 = shape2(e2), shape2 = shape1(e2)) is returned, else the default method is used; exact

*

signature(e1 = "UnivariateDistribution", e2 = "numeric") result again of class "UnivariateDistribution"; exact

*

signature(e1 = "AbscontDistribution", e2 = "numeric") result of class "AffLinAbscontDistribution"; exact

*

signature(e1 = "DiscreteDistribution", e2 = "numeric") result of class "AffLinDiscreteDistribution"; exact

*

signature(e1 = "LatticeDistribution", e2 = "numeric") result of class "AffLinLatticeDistribution"; exact

*

signature(e1 = "UnivarLebDecDistribution", e2 = "numeric") result of class "AffLinUnivarLebDecDistribution"; exact

*

signature(e1 = "CompoundDistribution", e2 = "numeric") result of class "AffLinUnivarLebDecDistribution"; exact

*

signature(e1 = "AffLinAbscontDistribution", e2 = "numeric") result again of class "AffLinAbscontDistribution"; exact

*

signature(e1 = "AffLinDiscreteDistribution", e2 = "numeric") result again of class "AffLinDiscreteDistribution"; exact

*

signature(e1 = "AffLinLatticeDistribution", e2 = "numeric") result again of class "AffLinLatticeDistribution"; exact

*

signature(e1 = "AffLinUnivarLebDecDistribution", e2 = "numeric") result of class "AffLinUnivarLebDecDistribution"; exact

*

signature(e1 = "DExp", e2 = "numeric") if abs(e2)>0 result again of class "DExp"; 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 = "Weibull", e2 = "numeric") if e2>0 result of class "Weibull"; exact

*

signature(e1 = "Cauchy", e2 = "numeric") if abs(e2)>0 result again of class "Cauchy"; exact

*

signature(e1 = "Dirac", e2 = "numeric") result again of class "Dirac"; exact

*

signature(e1 = "Norm", e2 = "numeric") if abs(e2)>0 result again of class "Norm"; exact

*

signature(e1 = "Unif", e2 = "numeric") if abs(e2)>0 result again of class "Unif"; exact

*

signature(e1 = "Logis", e2 = "numeric") if e2>0 result again of class "Logis"; exact

*

signature(e1 = "Lnorm", e2 = "numeric") if e2>0 result again of class "Lnorm"; 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 = "AcDcLcDistribution", e2 = "AcDcLcDistribution"): both operands are coerced to class "UnivarLebDecDistribution" and the corresponding method is used.

+

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 = "LatticeDistribution", e2 = "LatticeDistribution") assumes e1, e2 independent; if the larger lattice-width is an integer multiple of the smaller(in abs. value) one: result again of class "LatticeDistribution"; is generated by D/FFT

+

signature(e1 = "DiscreteDistribution", e2 = "DiscreteDistribution") assumes e1, e2 independent; result again of class "DiscreteDistribution"; is generated by explicite convolution

+

signature(e1 = "LatticeDistribution", e2 = "DiscreteDistribution") assumes e1, e2 independent; result again of class "DiscreteDistribution"; is generated by explicite convolution

+

signature(e1 = "UnivarLebDecDistribution", e2 = "UnivarLebDecDistribution") assumes e1, e2 independent; result again of class "UnivarLebDecDistribution"; is generated by separate explicite convolution of a.c. and discrete parts of e1 and e2 and subsequent flattening with flat.LCD; if getdistrOption("withSimplify") is TRUE, result is piped through a call to simplifyD

+

signature(e1 = "AcDcLcDistribution", e2 = "AcDcLcDistribution"): both operands are coerced to class "UnivarLebDecDistribution" and the corresponding method is used.

+

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 = "Cauchy", e2 = "Cauchy") assumes e1, e2 independent; result again of class "Cauchy"; uses the convolution formula for Cauchy 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 = "DiscreteDistribution") 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 = "AcDcLcDistribution", e2 = "AcDcLcDistribution"): by means of decomposePM e1 and e2 are decomposed into positive and negative parts; of these, convolutions of the corresponding logarithms are computed separately and finally exp is applied to them, again separately; the resulting mixing components are then flattened'' to one object of class UnivarLebDecDistribution by flat.LCD which according to getdistrOption(withSimplify) gets piped through a call to simplifyD.

/

signature(e1 = "Dirac", e2 = "Dirac") result again of class "Dirac"; exact

/

signature(e1 = "numeric", e2 = "Dirac") result again of class "Dirac"; exact

/

signature(e1 = "numeric", e2 = "AcDcLcDistribution"): if d.discrete(e2)(0)*discreteWeight(e2)>0 throws an error (would give division by 0 with positive probability); else by means of decomposePM e2 is decomposed into positive and negative parts; then, similarly the result obtains as for "*"(signature(e1 = "AcDcLcDistribution", e2 = "AcDcLcDistribution")) by the exp-log trick and is flattened'' to one object of class UnivarLebDecDistribution by flat.LCD and according to getdistrOption(withSimplify) is piped through a call to simplifyD; exact..

/

signature(e1 = "AcDcLcDistribution", e2 = "AcDcLcDistribution"): translated to e1 * (1/e2).

^

signature(e1 = "AcDcLcDistribution", e2 = "Integer"): if e2=0 returns Dirac(1); if e2=1 returns e1; if e2<0 translated to (1/e1)^(-e2); exact.

^

signature(e1 = "AcDcLcDistribution", e2 = "numeric"): if e2 is integer uses preceding item; else if e1< 0 with positive probability, throughs an error; else the result obtains similarly to "*"(signature(e1 = "AcDcLcDistribution", e2 = "AcDcLcDistribution")) by the exp-log trick and is flattened'' to one object of class UnivarLebDecDistribution by flat.LCD and according to getdistrOption(withSimplify) is piped through a call to simplifyD; exact.

^

signature(e1 = "AcDcLcDistribution", e2 = "AcDcLcDistribution"): if e1 is negative with positive probability, throws an error if e2 is non-integer with positive probability; if e1 is 0 with positive probability throws an error if e2 is non-integer with positive probability. if e2 is integer with probability 1 uses DiscreteDistribution(supp=e1^(Dirac(x)) for each x in support(e2), builds up a corresponding mixing distribution; the latter is flattened'' to one object of class UnivarLebDecDistribution by flat.LCD and according to getdistrOption(withSimplify) is piped through a call to simplifyD. Else the result obtains similarly to "*"(signature(e1 = "AcDcLcDistribution", e2 = "AcDcLcDistribution")) by the exp-log trick and is flattened'' to one object of class UnivarLebDecDistribution by flat.LCD and according to getdistrOption(withSimplify) is piped through a call to simplifyD; exact.

^

signature(e1 = "numeric", e2 = "AcDcLcDistribution"): if e1 is negative, throws an error if e2 is non-integer with positive probability; if e1 is 0 throws an error if e2 is non-integer with positive probability. if e2 is integer with probability 1 uses DiscreteDistribution(supp=e1^support(e2), prob=discrete.d(supp)) else the result obtains similarly to "*"(signature(e1 = "AcDcLcDistribution", e2 = "AcDcLcDistribution")) by the exp-log trick and is flattened'' to one object of class UnivarLebDecDistribution by flat.LCD and according to getdistrOption(withSimplify) is piped through a call to simplifyD; exact.

##### References

Ruckdeschel, P., Kohl, M.(2014): General purpose convolution algorithm for distributions in S4-Classes by means of FFT. J. Statist. Softw. 59(4): 1-25.

UnivariateDistribution-class AbscontDistribution-class DiscreteDistribution-class LatticeDistribution-class Norm-class Binom-class Pois-class Dirac-class Cauchy-class Gammad-class Logis-class Lnorm-class Exp-class Weibull-class Nbinom-class

##### Aliases
• operators-methods
• operators
• -,UnivariateDistribution,missing-method
• -,LatticeDistribution,missing-method
• -,Norm,missing-method
• +,UnivariateDistribution,numeric-method
• +,AbscontDistribution,numeric-method
• +,DiscreteDistribution,numeric-method
• +,LatticeDistribution,numeric-method
• +,UnivarLebDecDistribution,numeric-method
• +,AffLinAbscontDistribution,numeric-method
• +,AffLinDiscreteDistribution,numeric-method
• +,AffLinLatticeDistribution,numeric-method
• +,AffLinUnivarLebDecDistribution,numeric-method
• +,CompoundDistribution,numeric-method
• +,Cauchy,numeric-method
• +,Dirac,numeric-method
• +,Norm,numeric-method
• +,Unif,numeric-method
• +,numeric,UnivariateDistribution-method
• +,numeric,LatticeDistribution-method
• -,UnivariateDistribution,numeric-method
• -,UnivariateDistribution,UnivariateDistribution-method
• -,LatticeDistribution,numeric-method
• -,LatticeDistribution,LatticeDistribution-method
• -,LatticeDistribution,UnivariateDistribution-method
• -,UnivariateDistribution,LatticeDistribution-method
• -,AcDcLcDistribution,AcDcLcDistribution-method
• -,numeric,UnivariateDistribution-method
• -,numeric,LatticeDistribution-method
• *,UnivariateDistribution,numeric-method
• *,AbscontDistribution,numeric-method
• *,DiscreteDistribution,numeric-method
• *,LatticeDistribution,numeric-method
• *,UnivarLebDecDistribution,numeric-method
• *,CompoundDistribution,numeric-method
• *,AffLinAbscontDistribution,numeric-method
• *,AffLinDiscreteDistribution,numeric-method
• *,AffLinLatticeDistribution,numeric-method
• *,AffLinUnivarLebDecDistribution,numeric-method
• *,DExp,numeric-method
• *,Exp,numeric-method
• *,ExpOrGammaOrChisq,numeric-method
• *,Weibull,numeric-method
• *,Cauchy,numeric-method
• *,Dirac,numeric-method
• *,Norm,numeric-method
• *,Logis,numeric-method
• *,Lnorm,numeric-method
• *,Unif,numeric-method
• *,numeric,UnivariateDistribution-method
• *,numeric,LatticeDistribution-method
• /,UnivariateDistribution,numeric-method
• /,LatticeDistribution,numeric-method
• +,UnivariateDistribution,UnivariateDistribution-method
• +,AbscontDistribution,AbscontDistribution-method
• +,AbscontDistribution,DiscreteDistribution-method
• +,DiscreteDistribution,AbscontDistribution-method
• +,DiscreteDistribution,DiscreteDistribution-method
• +,LatticeDistribution,DiscreteDistribution-method
• +,LatticeDistribution,LatticeDistribution-method
• +,UnivarLebDecDistribution,UnivarLebDecDistribution-method
• +,AcDcLcDistribution,AcDcLcDistribution-method
• +,Binom,Binom-method
• +,Cauchy,Cauchy-method
• +,Chisq,Chisq-method
• +,Dirac,Dirac-method
• +,ExpOrGammaOrChisq,ExpOrGammaOrChisq-method
• +,Pois,Pois-method
• +,Nbinom,Nbinom-method
• +,Norm,Norm-method
• +,Logis,numeric-method
• +,Dirac,UnivariateDistribution-method
• +,Dirac,DiscreteDistribution-method
• +,UnivariateDistribution,Dirac-method
• -,numeric,Beta-method
• -,Dirac,Dirac-method
• *,Dirac,Dirac-method
• *,Dirac,UnivariateDistribution-method
• *,UnivariateDistribution,Dirac-method
• *,AcDcLcDistribution,AcDcLcDistribution-method
• /,Dirac,Dirac-method
• /,numeric,Dirac-method
• /,numeric,AcDcLcDistribution-method
• /,AcDcLcDistribution,AcDcLcDistribution-method
• ^,AcDcLcDistribution,numeric-method
• ^,AcDcLcDistribution,Integer-method
• ^,AcDcLcDistribution,AcDcLcDistribution-method
• ^,numeric,AcDcLcDistribution-method
##### Examples
# NOT RUN {
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)
N * P
N / N
# }
# NOT RUN {
## takes a little time
N ^ P
# }
# NOT RUN {
1.2 ^ N
abs(N) ^ 1.3
# }

Documentation reproduced from package distr, version 2.8.0, License: LGPL-3

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