Talk:Gamma distribution

message: It currently reads:
: \frac y {Nk - 1} \pm \frac {y^2} {(Nk - 1)^2 (Nk - 2)}. 
which dimensionally doesn't make sense. The second part is the variance, not the standard deviation. So, it should read: 
: \frac y {Nk - 1} \pm \frac {y} {(Nk - 1) \sqrt{Nk - 2}}.  
— Preceding unsigned comment added by GregorRitter (talk • contribs) 14:47, 14 May 2018 (UTC)
thread_title:  Error in Section 'Bayesian minimum mean squared error'

message: I've done a bit more on my explorations, and wrote up a paper that's now on math arXiv:  "Closed-form Tight Bounds and Approximations for the Median of a Gamma Distribution".  The main point here is that without any numerical work, closed forms can be derived that give great results.  It's also submitted to a journal, so with luck I'll get a peer-reviewed publication that's worth referencing for good median bounds and/or approximations.  Comments would be welcome.  Dicklyon (talk) 03:00, 11 November 2020 (UTC)
thread_title: Closed-from bounds and approximations to the median

message: I've updated the section Gamma distribution#Median approximations and bounds to represent the state of knowledge of bounds and asymptotic approximations, as published through early 2021, including a plot that represents the remaining big gap between bounds that my work attempts to fill.  Maybe if/when my paper gets published, someone will take a look and decide it worth adding something from it, even though the new bounds are characterized as "conjectures", lacking rigorous proof. Dicklyon (talk) 20:12, 9 May 2021 (UTC)
thread_title: Updated section

message: I've got a tentative acceptance on a new paper that proves some of the above bounds rigorously.  It will be a while before I fix the nits and get it published. Dicklyon (talk) 22:27, 30 May 2023 (UTC)
thread_title: The Lyon 2023 proofs

message: In the section listing connections with related distributions, it is not clear whether in Gamma(n, λ), λ is the scale or the rate of the Gamma distribution. To make things worse, it is used inconsistently in the first and second bullet point.
clearly the second is just a special case of the first property, yet the first one refers to the rate while the second to the scale. Original below:
-------------------------------------------------------------
* Let  X_1, X_2 \ldots X_n  be  n  independent and identically distributed random variables following an exponential distribution with rate parameter λ, then \sum_i  X_i ~ Gamma(n, λ).
* If X ~ Gamma(1, 1/λ) (shape -scale parametrization), then X has an exponential distribution with rate parameter λ.
--------------------------------------------------------------
I suggest picking one notation and using it consistently in the article, and also mentionning it everytime it is used. as in:
--------------------------------------------------------------
* Let  X_1, X_2 \ldots X_n  be  n  independent and identically distributed random variables following an exponential distribution with rate parameter λ, then \sum_i  X_i ~ Gamma(n, 1/λ) where n is the shape parameter and 1/λ is the scale.
* If X ~ Gamma(1, 1/λ) (shape -scale parametrization), then X has an exponential distribution with rate parameter λ.
--------------------------------------------------------------  — Preceding unsigned comment added by 105.99.140.18 (talk) 14:56, 14 December 2019 (UTC)
replies: text: Done.  Thanks, sorry it took me so long. Dicklyon (talk) 20:01, 4 April 2020 (UTC)
thread_title:  Scale vs. Rate in the "Related Distributions" Section 

message: I believe an edit is needed to the Gamma distribution page. In the Method of Moments text box at the top of the page, please add: 
 \theta = \frac {V[X]} {E[X]} ,  k=  \frac {E[X]^2} {V[X]}. 
Information to be added:  \theta = \frac {V[X]} {E[X]} ,  k=  \frac {E[X]^2} {V[X]}. 
Explanation of issue: If you calculate k and theta using the mean and variance stated, you can get the following method of moments estimators for theta and k. 
References supporting change: Solve the system of equations:
mean = k * θ =>  k = \frac {mean} {\theta} 
Replace k in terms of theta:
variance = k*\theta^2  => variance = \frac {mean} {\theta} *\theta^2   = mean * θ => θ = \frac {variance} {mean}  =>  \theta = \frac {V[X]} {E[X]} 
Then solve mean equation for k replacing θ with variance/mean. 
mean=  k*\frac{variance}{mean} => k = \frac {mean} {\frac{variance}{mean}} => k = \frac {mean^2} {variance}   =>  k=  \frac {E[X]^2} {V[X]}. 
James Tourkistas — Preceding unsigned comment added by Jtourkis (talk • contribs) 22:54, 12 August 2020 (UTC)
replies: text: Done, though apparently that template doesn't support a moments2 parameter for an alternate, so I kludged it.  Will look further... Dicklyon (talk) 00:57, 13 August 2020 (UTC)

text: Fixed now by the good template hacker. Dicklyon (talk) 19:25, 13 August 2020 (UTC)
thread_title:  Gamma distribution Method of Moments Estimators 

message: In this article, the distribution is referred to variously as
* \gamma(\alpha,\beta)
* \Gamma(\alpha,\beta)
* \operatorname{Gamma}(\alpha,\beta)
There seems to be now relation as to whether parametrisations are intended with rate or scale. 
Shouldn't this be harmonized throughout the article? Deviating notation used in other texts should be pointed out in one place, and one notation should be used consistently in this article.
Moreover, it seems to me that in a few other texts, \beta is also used when scale instead of rate is intended, so perhaps one should mention as a caveat that people don't follow these naming conventions strictly.
In particular, Microsoft Excel is very widely used software and it uses a different terminology to that in the article. I suggest adding to the article "Note that Microsoft Excel uses the shape / scale parameterization but calls them alpha and beta." This is very confusing!  Source: https://support.microsoft.com/en-gb/office/gamma-dist-function-9b6f1538-d11c-4d5f-8966-21f6a2201def  — Preceding unsigned comment added by Blitzer99 (talk • contribs) 15:06, 13 March 2024 (UTC)
thread_title:  Notation 

message: Maybe gammacdf should be 1-F(x) given in the page 201.231.180.105 (talk) 14:13, 5 April 2023 (UTC)
thread_title:  CDF