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 DFTUsage
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)
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