distr (version 2.0.6)

convpow-methods: Distribution of the sum of univariate i.i.d r.v's

Description

Method convpow determines the distribution of the sum of N univariate i.i.d r.v's by means of DFT

Usage

convpow(D1,...)
  ## S3 method for class 'AcDcLcDistribution':
convpow(D1,N)
  ## S3 method for class 'AbscontDistribution':
convpow(D1,N)
  ## S3 method for class 'LatticeDistribution':
convpow(D1,N)
  ## S3 method for class 'DiscreteDistribution':
convpow(D1,N)
  ## S3 method for class 'AcDcLcDistribution':
convpow(D1,N)

Arguments

D1

an object of (a sub)class (of) "AbscontDistribution" or "LatticeDistribution" or of "UnivarLebDecDistribution"

...

not yet used; meanwhile takes up N

N

an integer or 0 (for 0 returns Dirac(0), for 1 D1)

Value

• Object of class "AbscontDistribution", "DiscreteDistribution", "LatticeDistribution" resp. "AcDcLcDistribution"

concept

• convolution for distributions
• arithmetics for distributions
• info file
• FFT
• DFT

Details

in the methods implemented a second argument N is obligatory; the general methods use a general purpose convolution algorithm for distributions by means of D/FFT. In case of an argument of class "UnivarLebDecDistribution", the result will in generally be again of class "UnivarLebDecDistribution". However, if acWeight(D1) is positive, discreteWeight(convpow(D1,N)) will decay exponentially in N, hence from some (small) $N_0$ on, the result will be of class "AbscontDistribution". This is used algorithmically, too, as then only the a.c. part needs to be convolved. In case of an argument D1 of class "DiscreteDistribution", for N equal to 0,1 we return the obvious solutions, and for N==2 the return value is D1+D1. For N>2, we split up N into N=N1+N2, N1=floor(N/2) and recursively return convpow(D1,N1)+convpow(D1,N2).

References

Kohl, M., Ruckdeschel, P., Stabla, T. (2005): General purpose convolution algorithm for distributions in S4-Classes by means of FFT. Technical report, Feb. 2005. Also available in http://www.uni-bayreuth.de/departments/math/org/mathe7/RUCKDESCHEL/pubs/comp.pdf

See Also

operators, distrARITH()

Examples

convpow(Exp()+Pois(),4)