[R] convolution of the double exponential distribution

[Matthias Kohl]

Hi David,

you can even increase the precision of these computations by changing 
the variables
"DefaultNrFFTGridPointsExponent" (default: 12 -> 2^12 grid points) and 
"TruncQuantile"
(default: 1e-5) in our package "distr"; see
distroptions()

You can for instance use

distroptions("DefaultNrFFTGridPointsExponent", 14)
and
distroptions("TruncQuantile", 1e-8)

We checked our algorithm in case of Binomial, Poisson, Normal and 
Exponential distributions and found a very high precision; confer 
Section 5 of

http://www.stamats.de/comp.pdf

Moreover, for n-fold convolutions you can also use the function 
"convpow" which can be found under
http://www.uni-bayreuth.de/departments/math/org/mathe7/DISTR/nFoldConvolution.R

hth,
Matthias

>Ravi, Duncan, and Matthias,
>
>Thank you very much for the helpful replies. For convolutions with 2 or
>3 copies, I found that the CDFs from the distr package closely match the
>analytic results from this paper:
>K. Singh, M. Xie, and W. E. Strawderman, "Combining Information From
>Independent Sources Through Confidence Distributions," Annals of
>Statistics 33, no. 1 (2005): 159-183.
>
>That gives me confidence that the package will also work well for higher
>copy numbers. At least for me, using the package is much more convenient
>than programming all the needed integrals into R.
>
>David
>_______________________________________
>David R. Bickel  http://davidbickel.com
>Research Scientist
>Pioneer Hi-Bred International (DuPont)
>Bioinformatics and Exploratory Research
>7200 NW 62nd Ave.; PO Box 184
>Johnston, IA 50131-0184
>515-334-4739 Tel
>515-334-4473 Fax
>david.bickel at pioneer.com, bickel at prueba.info
>
>
>| -----Original Message-----
>| From: Matthias Kohl [mailto:Matthias.Kohl at stamats.de] 
>| Sent: Friday, December 23, 2005 9:09 AM
>| To: Bickel, David
>| Cc: Duncan Murdoch; r-help at stat.math.ethz.ch
>| Subject: Re: [R] convolution of the double exponential distribution
>| 
>| Duncan Murdoch schrieb:
>| 
>| >On 12/22/2005 7:56 PM, Bickel, David wrote:
>| >  
>| >
>| >>Is there any R function that computes the convolution of the double
>| >>exponential distribution?
>| >>
>| >>If not, is there a good way to integrate ((q+x)^n)*exp(-2x) 
>| over x from
>| >>0 to Inf for any value of q and for any positive integer n? 
>| I need to
>| >>perform the integration within a function with q and n as 
>| arguments. The
>| >>function integrate() is giving me this message:
>| >>
>| >>"evaluation of function gave a result of wrong length"
>| >>    
>| >>
>| >
>| >Under the substitution of y = q+x, that looks like a gamma integral. 
>| >The x = 0 to Inf range translates into y = q to Inf, so 
>| you'll need an 
>| >incomplete gamma function, such as pgamma.  Be careful to get the 
>| >constant multiplier right.
>| >
>| >Duncan Murdoch
>| >
>| >______________________________________________
>| >R-help at stat.math.ethz.ch mailing list
>| >https://stat.ethz.ch/mailman/listinfo/r-help
>| >PLEASE do read the posting guide! 
>| http://www.R-project.org/posting-guide.html
>| >  
>| >
>| 
>| Hi,
>| 
>| you can use our package "distr".
>| 
>| require(distr)
>| ## define double exponential distribution
>| loc <- 0 # location parameter
>| sca <- 1 # scale parameter
>| 
>| rfun <- function(n){ loc + scale * ifelse(runif(n) > 0.5, 1, 
>| -1) * rexp(n) }
>| body(rfun) <- substitute({ loc + scale * ifelse(runif(n) > 
>| 0.5, 1, -1) * 
>| rexp(n) },
>|                          list(loc = loc, scale = sca))
>| 
>| dfun <- function(x){ exp(-abs(x-loc)/scale)/(2*scale) }
>| body(dfun) <- substitute({ exp(-abs(x-loc)/scale)/(2*scale) 
>| }, list(loc 
>| = loc, scale = sca))
>| 
>| pfun <- function(x){ 0.5*(1 + 
>| sign(x-loc)*(1-exp(-abs(x-loc)/scale))) }
>| body(pfun) <- substitute({ 0.5*(1 + 
>| sign(x-loc)*(1-exp(-abs(x-loc)/scale))) },
>|                          list(loc = loc, scale = sca))
>|                         
>| qfun <- function(x){ loc - scale*sign(x-0.5)*log(1 - 2*abs(x-0.5)) }
>| body(qfun) <- substitute({ loc - scale*sign(x-0.5)*log(1 - 
>| 2*abs(x-0.5)) },
>|                          list(loc = loc, scale = sca))
>| 
>| D1 <- new("AbscontDistribution", r = rfun, d = dfun, p = 
>| pfun, q = qfun)
>| plot(D1)
>| 
>| D2 <- D1 + D1 # convolution based on FFT
>| plot(D2)
>| 
>| hth,
>| Matthias
>| 
>| -- 
>| StaMatS - Statistik + Mathematik Service
>| Dipl.Math.(Univ.) Matthias Kohl
>| www.stamats.de
>| 
>
>This communication is for use by the intended recipient and ...{{dropped}}
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
>  
>


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