[R] E(1/(X+c)) ? where X ~ Chi-square(n) and c is a constant.

[Spencer Graves]

	  In case you don't already have all this, permit me to identify it as 
a confluent hypergeometric function.  Abramowitz and Stegun (1964) 
Handbook of Mathematical Functions (National Bureau of Standard, Applied 
Math Series 55, expression 13.2.5):

Gamma(a)U(a, b, z) =
integral{over t=0 to Inf of
exp(-z*t)*((t^(a-1))*((1+t)^(b-a-1))*dt}

See also Luke (1969) The Special Functions and their Approximations, 
vol. I (Academic Press, p. 116, sec. 4.2, expr. (7)).

	  It is probably contained in any book that discusses the confluent 
hypergeometric function.

	  I would write the chi-square as a gamma distribution, then factor out 
the "c" in your expression, then change variables to get an integral of 
this form.

	  Abramowitz and Stegun is available on the web.  I felt the need to 
download two different versions, because one was searchable but 
incomplete while the other was complete but not searchable.  See, e.g., 
"www.math.sfu.ca/~cbm/aands".

	  hope this helps,
	  Spencer Graves

MARK LEEDS wrote:
> i don't know it off the top of my head but there's a relation between powers 
> of the chi squared and the gamma dsitribution.
> check it out in casella and berger or arnold.
> 
>                                                                              
>                         mark
> 
> 
> ----- Original Message ----- 
> From: "Philip He" <hydinghua at gmail.com>
> To: <r-help at stat.math.ethz.ch>
> Sent: Monday, May 15, 2006 2:52 PM
> Subject: [R] E(1/(X+c)) ? where X ~ Chi-square(n) and c is a constant.
> 
> 
>> Hi all,
>>
>> Can someone help me with the following expectation in a closed form?
>>
>> E(1/(X+c))
>>
>> where X ~ Chi-square(n) and c is a constant.
>>
>> Thanks.
>>
>> [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> 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
>>
> 
> ______________________________________________
> 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