[R] convolution of the double exponential distribution
Erich Neuwirth
erich.neuwirth at univie.ac.at
Fri Dec 23 18:23:41 CET 2005
Mathematica says
Assuming[q âˆˆ Reals && q > 0, Integrate[(q + x)^n*Exp[-2*x], {x, 0,
Infinity}]]
2^(-1 - n)*Exp[2*q]*Gamma[1 + n, 2*q]
and 2-argument Gamma is the incomplete Gamma function
(integration starting at 2*q)
Duncan Murdoch wrote:
> 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
>
>
--
Erich Neuwirth, University of Vienna
Faculty of Computer Science
Computer Supported Didactics Working Group
Visit our SunSITE at http://sunsite.univie.ac.at
Phone: +43-1-4277-38624 Fax: +43-1-4277-9386
More information about the R-help
mailing list