Talk:Inverse-gamma distribution

message: In characteristic function for this distribution, there is a function K_alpha. What is this? What is it called?  —Preceding unsigned comment added by 95.72.39.82 (talk) 22:34, 2 March 2009 (UTC)
thread_title:  K_alpha function 

message: I changed the mfg to "Does not exist" because it doesn't exist. Richard Finlay
Basmandude 16:05, 27 July 2006 (UTC)
thread_title:  mfg change 

message: The gnuplot source for the CDF figure is given as:
 pinvgamma(x,a,b) = 1 - igamma(a, b*1.0/x)
but it seems to me that the CDF should actually be:
 pinvgamma(x,a,b) = 1 - igamma(a, b*1.0/x) / gamma(a)
if igamma is the lower incomplete gamma function, since we have:
:\frac{\Gamma(\alpha,x)}{\Gamma(a)} = 1 - \frac{\gamma(\alpha,x)}{\Gamma(a)}
from Incomplete gamma function.
Ged.R 12:03, 8 March 2007 (UTC)
thread_title:  CDF figure incorrect? 

message: Shouldn't there be a reference to the scaled inverse gamma distribution? I am not a statistitian so I do not feel comfortable explaining the differences. The difference is just a transformation or a substitution? Thanks. --Kupirijo 16:30, 31 March 2007 (UTC)
thread_title:  Scaled inverse gamma distribution 

message: I think it should be  \tau  instead of \sigma since \sigma is usually used for standard deviations but here it is used as precision, which is usually labeled  \tau . 129.26.160.2 11:39, 14 September 2007 (UTC)
thread_title:  naming conventions 

message: Maybe I'm missing something obvious but shouldn't it be
If X \sim \mbox{Inv-Gamma}(k, \theta)\, , then 1/X \sim \mbox{Gamma}(k, \theta) \, , is a Gamma distribution.
Thenegus 13:15, 28 September 2007 (UTC)
thread_title:  Related Distributions Typo? 

message: The article is not really a good one and does not quite give the inverse-gamma the credit its due. The formula for the density was wrong; the correct version is proportional to 
(1/x)^{\alpha + 1}\exp(-\beta/x). The `moment-generating function' is a bit odd to include, as it does not exist for any positive t (only for negative t, and zero); it's better to erase it and to include the Laplace transform. Also, it is mildly dangerous to give a formula in terms of a certain `K_\alpha' function without any further pointer to what this function actually is. Slavatrudu (talk) 18:19, 24 April 2008 (UTC)
thread_title:  The article needs some cleaning 

message: Does K_\alpha mean the Bessel function? But what concerns the moment generating function, this is wrong, since it does not exist.  —Preceding unsigned comment added by 194.145.96.51 (talk) 09:47, 4 June 2010 (UTC)
thread_title:  mgf @ cf 

message: should the parameters alpha and beta include zero
so alpha >= 0 rather than alpha > 0
This seems consistent with the supported range?
And a velue of zero seems reasonable.  —Preceding unsigned comment added by Pabristow (talk • contribs) 13:59, 3 September 2010 (UTC)
thread_title:  should the parameters alpha and beta range include zero 

message: In the "Derivation from the gamma distribution" section, the page notes
>Note that beta is the scale parameter from the perspective of the inverse gamma distribution.
This seems to be unclear without additional justification.  What is meant by this exactly? Phdemetri (talk) 20:43, 26 August 2022 (UTC)
replies: text: A parameter θ of a family of distributions is a "scale parameter" if the following holds. If two variables x and y have distributions from that family, differing only in having different values of θ, say θ1 and θ2, then the distribution of x is the same as that of y "scaled" by being multiplied by the factor θ1/θ2. Probably the best known example is the standard deviation σ in the case of a normal distribution: changing the value of σ scales the distribution without changing its shape. Evidently "β is the scale parameter from the perspective of the inverse gamma distribution" is intended to mean that β serves as a scale factor in the inverse gamma distribution, whereas it is not a scale parameter in the gamma distribution. As with a lot of mathematical articles on Wikipedia, this was no doubt written by a mathematician writing for other mathematicians with a similar background knowledge of the same subject area, without regard for the general reader. It could no doubt be better written, but I don't have time to do that now. I may or may not come back to it. JBW (talk) 21:06, 26 August 2022 (UTC)
replies: text: I made a small edit to the page to demonstrate that beta satisfies the conditions for being called a scale parameter, linking to the scale parameter wiki page.  Feel free to edit it if you feel necessary for content or formatting. Phdemetri (talk) 22:24, 26 August 2022 (UTC)
thread_title:  What is meant by beta being the scale parameter with respect to the inverse gamma distirbution?