distr (version 2.7.0)

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,...)
  # S4 method for AbscontDistribution
convpow(D1,N)
  # S4 method for LatticeDistribution
convpow(D1,N, 
                     ep = getdistrOption("TruncQuantile"))
  # S4 method for DiscreteDistribution
convpow(D1,N)
  # S4 method for AcDcLcDistribution
convpow(D1,N, 
                     ep = getdistrOption("TruncQuantile"))

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)

ep

numeric of length 1 in (0,1) --- for "LatticeDistribution": support points will be cancelled if their probability is less than ep; for "UnivarLebDecDistribution": if (acWeight(object)<ep) we work with the discrete parts only, and, similarly, if (discreteWeight(object)<ep) we with the absolutely continuous parts only.

Value

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

further S4-Methods

There are particular methods for the following classes, using explicit convolution formulae:

signature(D1="Norm")

returns class "Norm"

signature(D1="Nbinom")

returns class "Nbinom"

signature(D1="Binom")

returns class "Binom"

signature(D1="Cauchy")

returns class "Cauchy"

signature(D1="ExpOrGammaOrChisq")

returns class "Gammad" ---if D1 may be coerced to Gammad

signature(D1="Pois")

returns class "Pois"

signature(D1="Dirac")

returns class "Dirac"

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

See Also

operators, distrARITH()

Examples

# NOT RUN {
convpow(Exp()+Pois(),4)
# }