# Re: [R] convolution of the double exponential distribution

From: Matthias Kohl <Matthias.Kohl_at_stamats.de>
Date: Sat 24 Dec 2005 - 02:08:30 EST

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
>
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>

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

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