Talk:Gompertz function

Sigmoidal shape depends on parameter

In the current parameterization, if c is positive and b is positive, the function grows without bound. If c is positive but b is negative, then the function converges to 0 from above as t increases. This last case corresponds most closely to Gompertz's mortality law.

Problem with images

We need to make clear that the right asymptote is not horizontal, while the left is. 99.35.128.24 (talk) 16:40, 29 July 2009 (UTC)

On second thought, I think I may be wrong about this, but I think I have a good reason for making the mistake. I asked on the Math Reference Desk. 99.35.128.24 (talk) 17:01, 29 July 2009 (UTC)

right asymptote

Is it better to say that the horizontal right asymptote can be approached much more gradually than the left? HowDoIUseUnifiedLogin? (talk) 18:47, 29 July 2009 (UTC)

Relationship to Gumbel distribution

I've been working on some sequence alignment statistics problems which make use of the extreme value distribution, which is also the Gumbel distribution. After looking at some curve fitting tools I came across this Gompertz function, and it turns out the two are exactly the same assuming a=1 and b and c are negative. Gumbel is written differently, but the functions are equivalent. It would seem sensible to make a note of this, perhaps in the "Example uses" section.

Also, it could be useful to provide variations of how the equation is presented in the other uses. For instance, here we have a*exp(b*exp(c*t)); but it could also be written as a*exp(exp(b*(t-c))) or with some other variation which would make it recognizable to someone who had seen it written in a different way. For example, Gumbel uses exp(-exp(t-mu)/beta), alignment statistics people use exp(-Kmn*exp(lambda*t)) (where beta = 1/lambda; and mu=ln(Kmn)/lambda). Tgillet1 (talk) 22:30, 27 April 2011 (UTC)

References

Clarified the role of b, but want to make sure what I wrote is accurate

I was initially confused about the role of the b parameter until a friend explained it to me. The previous version of the page (before I changed it) said "b sets the y displacement," which I think is technically correct but I found confusing. Changing the value of b causes the entire graph to move to the right or left. So I Was Bold and changed the description. But my knowledge of math is shaky enough that I could be wrong about this, so I wanted to flag the change on the Talk page.

Raddick (talk) 19:54, 5 December 2013 (UTC)

Express b and c as positive or negative?

The article expresses the formula for the Gompertz function as

$y(t)=ae^{be^{ct}}$

...and specifies that b and c must be negative. I've seen other online references instead give the formula as

$y(t)=ae^{-be^{-ct}}$

...while specifying that b and c should be positive.

Obviously it's the same function either way, but I find it a little clearer to use the latter formulation, which makes it explicitly clear that the function calls for a positive input in a and negative inputs in b and c. (Otherwise, it's still a Gompertz function, I believe, but becomes unphysical for modeling real-world processes like population growth.)

I can Be Bold and make the change, but I think it's worth giving it a couple days to discuss here first.

Raddick (talk) 20:19, 5 December 2013 (UTC)

Actually, keeping it the way it is

I realized that to make this change, I would also need to change the included graphs to label b and c as positive there. That requires editing the original SVG files. This is a bit beyond my ability right now, so I'll let it be. Although I've been meaning to learn SVG editing, so I may come back later and make this change. Thoughts welcome in the meantime.

Raddick (talk) 09:53, 11 December 2013 (UTC)

Expanding article

Hi, I am planning to expand and modify this page to include more information, especially in regards to applications. You can find my sandbox here: https://en.wikipedia.org/wiki/User:I9T1997/sandbox

So far I have modified your lead paragraph. — Preceding unsigned comment added by I9T1997 (talk • contribs) 22:47, 22 June 2018 (UTC)

Top picture is sigmoid not gomprertz, misleading search results

That causes Google to show the wrong function in search results, as shown in this image: https://drive.google.com/file/d/1Sg0xqgMUUJK5ra1OIQaMUNV6dL1NcKc0/view?usp=drivesdk. One some representative image of an actual gomprertz function should be shown first instead. ★NealMcB★ (talk) 21:12, 25 May 2021 (UTC)

Value of function when $t=0$ is $a/e^{2}$ not $a/2$

The Formula section states the following:

b sets the displacement along the x-axis (translates the graph to the left or right). When b = log(2), f(0) = a/2, also called the halfway point.

This is incorrect, when b = log(2) and t = 0, f(0) = a/e^2

Pirouzeh (talk) 17:51, 26 November 2021 (UTC)