Logistic function with a slope but no asymptotes?Has Arcsinh ever been considered as a neural network activation function?Effect of e when using the Sigmoid Function as an activation functionApproximation of Δoutput in context of Sigmoid functionModification of Sigmoid functionFinding the center of a logistic curveInput and Output range of the composition of Gaussian and Sigmoidal functions and it's entropyFinding the slope at different points in a sigmoid curveQuestion about Sigmoid Function in Logistic RegressionHas Arcsinh ever been considered as a neural network activation function?The link between logistic regression and logistic sigmoidHow can I even out the output of the sigmoid function?

Non-trope happy ending?

Why is so much work done on numerical verification of the Riemann Hypothesis?

Is this part of the description of the Archfey warlock's Misty Escape feature redundant?

Multiplicative persistence

What is Cash Advance APR?

Giving feedback to someone without sounding prejudiced

Why do ¬, ∀ and ∃ have the same precedence?

How to draw a matrix with arrows in limited space

Why does this expression simplify as such?

Doesn't the system of the Supreme Court oppose justice?

Will number of steps recorded on FitBit/any fitness tracker add up distance in PokemonGo?

Why can't the Brexit deadlock in the UK parliament be solved with a plurality vote?

Which was the first story featuring espers?

Does the reader need to like the PoV character?

Why is the "ls" command showing permissions of files in a FAT32 partition?

How much theory knowledge is actually used while playing?

15% tax on $7.5k earnings. Is that right?

How to preserve electronics (computers, iPads and phones) for hundreds of years

Did the UK lift the requirement for registering SIM cards?

Creating two special characters

Why does AES have exactly 10 rounds for a 128-bit key, 12 for 192 bits and 14 for a 256-bit key size?

Can I cause damage to electrical appliances by unplugging them when they are turned on?

Does an advisor owe his/her student anything? Will an advisor keep a PhD student only out of pity?

What is the English pronunciation of "pain au chocolat"?



Logistic function with a slope but no asymptotes?


Has Arcsinh ever been considered as a neural network activation function?Effect of e when using the Sigmoid Function as an activation functionApproximation of Δoutput in context of Sigmoid functionModification of Sigmoid functionFinding the center of a logistic curveInput and Output range of the composition of Gaussian and Sigmoidal functions and it's entropyFinding the slope at different points in a sigmoid curveQuestion about Sigmoid Function in Logistic RegressionHas Arcsinh ever been considered as a neural network activation function?The link between logistic regression and logistic sigmoidHow can I even out the output of the sigmoid function?













7












$begingroup$


The logistic function has an output range 0 to 1, and asymptotic slope is zero on both sides.



What is an alternative to a logistic function that doesn't flatten out completely at its ends? Whose asymptotic slopes are approaching zero but not zero, and the range is infinite?










share|cite|improve this question











$endgroup$







  • 2




    $begingroup$
    The title seems to disagree with how i read your question -- is this new function required to have asymptotes or not?
    $endgroup$
    – jld
    yesterday










  • $begingroup$
    Basically I want a function that looks like sigmoid but has a slope
    $endgroup$
    – Aksakal
    yesterday










  • $begingroup$
    I just updated -- is that more what you mean? I'm still not sure what you mean by a "slope". Do you mean a sigmoid shape but with $lim_xtopminftyf(x) = pm infty$, i.e. it doesn't flatten out into horizontal asymptotes at $|x|$ grows?
    $endgroup$
    – jld
    yesterday






  • 5




    $begingroup$
    $operatornamesign(x)log(1 + |x|)$?
    $endgroup$
    – steveo'america
    yesterday







  • 3




    $begingroup$
    Beginning of the decade called, it wants its neural network activation functions back. (Sorry bad joke, but realistically this is why people moved to ReLUs) (+1 though, relevant question)
    $endgroup$
    – usεr11852
    yesterday
















7












$begingroup$


The logistic function has an output range 0 to 1, and asymptotic slope is zero on both sides.



What is an alternative to a logistic function that doesn't flatten out completely at its ends? Whose asymptotic slopes are approaching zero but not zero, and the range is infinite?










share|cite|improve this question











$endgroup$







  • 2




    $begingroup$
    The title seems to disagree with how i read your question -- is this new function required to have asymptotes or not?
    $endgroup$
    – jld
    yesterday










  • $begingroup$
    Basically I want a function that looks like sigmoid but has a slope
    $endgroup$
    – Aksakal
    yesterday










  • $begingroup$
    I just updated -- is that more what you mean? I'm still not sure what you mean by a "slope". Do you mean a sigmoid shape but with $lim_xtopminftyf(x) = pm infty$, i.e. it doesn't flatten out into horizontal asymptotes at $|x|$ grows?
    $endgroup$
    – jld
    yesterday






  • 5




    $begingroup$
    $operatornamesign(x)log(1 + |x|)$?
    $endgroup$
    – steveo'america
    yesterday







  • 3




    $begingroup$
    Beginning of the decade called, it wants its neural network activation functions back. (Sorry bad joke, but realistically this is why people moved to ReLUs) (+1 though, relevant question)
    $endgroup$
    – usεr11852
    yesterday














7












7








7





$begingroup$


The logistic function has an output range 0 to 1, and asymptotic slope is zero on both sides.



What is an alternative to a logistic function that doesn't flatten out completely at its ends? Whose asymptotic slopes are approaching zero but not zero, and the range is infinite?










share|cite|improve this question











$endgroup$




The logistic function has an output range 0 to 1, and asymptotic slope is zero on both sides.



What is an alternative to a logistic function that doesn't flatten out completely at its ends? Whose asymptotic slopes are approaching zero but not zero, and the range is infinite?







sigmoid-curve






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 19 hours ago









Neil G

9,79012970




9,79012970










asked yesterday









AksakalAksakal

39k452120




39k452120







  • 2




    $begingroup$
    The title seems to disagree with how i read your question -- is this new function required to have asymptotes or not?
    $endgroup$
    – jld
    yesterday










  • $begingroup$
    Basically I want a function that looks like sigmoid but has a slope
    $endgroup$
    – Aksakal
    yesterday










  • $begingroup$
    I just updated -- is that more what you mean? I'm still not sure what you mean by a "slope". Do you mean a sigmoid shape but with $lim_xtopminftyf(x) = pm infty$, i.e. it doesn't flatten out into horizontal asymptotes at $|x|$ grows?
    $endgroup$
    – jld
    yesterday






  • 5




    $begingroup$
    $operatornamesign(x)log(1 + |x|)$?
    $endgroup$
    – steveo'america
    yesterday







  • 3




    $begingroup$
    Beginning of the decade called, it wants its neural network activation functions back. (Sorry bad joke, but realistically this is why people moved to ReLUs) (+1 though, relevant question)
    $endgroup$
    – usεr11852
    yesterday













  • 2




    $begingroup$
    The title seems to disagree with how i read your question -- is this new function required to have asymptotes or not?
    $endgroup$
    – jld
    yesterday










  • $begingroup$
    Basically I want a function that looks like sigmoid but has a slope
    $endgroup$
    – Aksakal
    yesterday










  • $begingroup$
    I just updated -- is that more what you mean? I'm still not sure what you mean by a "slope". Do you mean a sigmoid shape but with $lim_xtopminftyf(x) = pm infty$, i.e. it doesn't flatten out into horizontal asymptotes at $|x|$ grows?
    $endgroup$
    – jld
    yesterday






  • 5




    $begingroup$
    $operatornamesign(x)log(1 + |x|)$?
    $endgroup$
    – steveo'america
    yesterday







  • 3




    $begingroup$
    Beginning of the decade called, it wants its neural network activation functions back. (Sorry bad joke, but realistically this is why people moved to ReLUs) (+1 though, relevant question)
    $endgroup$
    – usεr11852
    yesterday








2




2




$begingroup$
The title seems to disagree with how i read your question -- is this new function required to have asymptotes or not?
$endgroup$
– jld
yesterday




$begingroup$
The title seems to disagree with how i read your question -- is this new function required to have asymptotes or not?
$endgroup$
– jld
yesterday












$begingroup$
Basically I want a function that looks like sigmoid but has a slope
$endgroup$
– Aksakal
yesterday




$begingroup$
Basically I want a function that looks like sigmoid but has a slope
$endgroup$
– Aksakal
yesterday












$begingroup$
I just updated -- is that more what you mean? I'm still not sure what you mean by a "slope". Do you mean a sigmoid shape but with $lim_xtopminftyf(x) = pm infty$, i.e. it doesn't flatten out into horizontal asymptotes at $|x|$ grows?
$endgroup$
– jld
yesterday




$begingroup$
I just updated -- is that more what you mean? I'm still not sure what you mean by a "slope". Do you mean a sigmoid shape but with $lim_xtopminftyf(x) = pm infty$, i.e. it doesn't flatten out into horizontal asymptotes at $|x|$ grows?
$endgroup$
– jld
yesterday




5




5




$begingroup$
$operatornamesign(x)log(1 + |x|)$?
$endgroup$
– steveo'america
yesterday





$begingroup$
$operatornamesign(x)log(1 + |x|)$?
$endgroup$
– steveo'america
yesterday





3




3




$begingroup$
Beginning of the decade called, it wants its neural network activation functions back. (Sorry bad joke, but realistically this is why people moved to ReLUs) (+1 though, relevant question)
$endgroup$
– usεr11852
yesterday





$begingroup$
Beginning of the decade called, it wants its neural network activation functions back. (Sorry bad joke, but realistically this is why people moved to ReLUs) (+1 though, relevant question)
$endgroup$
– usεr11852
yesterday











3 Answers
3






active

oldest

votes


















10












$begingroup$

Initially I was thinking you did want the horizontal asymptotes at $0$ still; I moved my original answer to the end. If you instead want $lim_xtopm infty f(x) = pminfty$ then would something like the inverse hyperbolic sine work?
$$
textasinh(x) = logleft(x + sqrt1 + x^2right)
$$



This is unbounded but grows like $log$ for large $|x|$ and looks like
asinh



I like this function a lot as a data transformation when I've got heavy tails but possibly zeros or negative values.



Another nice thing about this function is that $textasinh'(x) = frac1sqrt1+x^2$ so it has a nice simple derivative.




Original answer



$newcommandevarepsilon$Let $f : mathbb Rtomathbb R$ be our function and we'll assume
$$
lim_xtopm infty f(x) = 0.
$$



Suppose $f$ is continuous. Fix $e > 0$. From the asymptotes we have
$$
exists x_1 : x < x_1 implies |f(x)| < e
$$

and analogously there's an $x_2$ such that $x > x_2 implies |f(x)| < e$. Therefore outside of $[x_1,x_2]$ $f$ is within $(-e, e)$. And $[x_1,x_2]$ is a compact interval so by continuity $f$ is bounded on it.



This means that any such function can't be continuous. Would something like
$$
f(x) = begincases x^-1 & xneq 0 \ 0 & x = 0endcases
$$
work?






share|cite|improve this answer











$endgroup$








  • 1




    $begingroup$
    The "Related" threads include this unanswered question, in case anyone else has asked themselves the natural followup "what happens if you use asinh in a neural network?" stats.stackexchange.com/questions/359245/…
    $endgroup$
    – Sycorax
    yesterday











  • $begingroup$
    @Sycorax thanks, i was wondering about that
    $endgroup$
    – jld
    yesterday










  • $begingroup$
    My ears did indeed prick up. I have in the past found asinh() useful when you want to 'do log stuff' to both positive and negative numbers. It also gets around the quandry you can get in, where you need to do a log transform on data with zeros and have to judge an appropriate value of $a$ for $log(x + a)$
    $endgroup$
    – Ingolifs
    yesterday


















9












$begingroup$

You could just add a term to a logistic function:



$$
f(x; a, b, c, d, e)=fraca1+bexp(-cx) + dx + e
$$



The asymptotes will have slopes $d$.



Here is an example with $a=10, b = 1, c = 2, d = frac120, e = -5$:



Sigmoid






share|cite|improve this answer









$endgroup$








  • 1




    $begingroup$
    I think this answer is the best because if you zoom out far enough it's just a straight line with a little wiggle in the middle. Gives the most intuitive behavior at large x but retains the sigmoid shape.
    $endgroup$
    – user1717828
    yesterday


















5












$begingroup$

I will go ahead and turn the comment into an answer. I suggest
$$
f(x) = operatornamesign(x)logright),
$$

which has slope tending towards zero, but is unbounded.



edit by popular demand, a plot, for $|x|le 30$:
enter image description here






share|cite|improve this answer











$endgroup$








  • 2




    $begingroup$
    a graph of the function would be useful
    $endgroup$
    – qwr
    18 hours ago










  • $begingroup$
    @qwr and done...
    $endgroup$
    – steveo'america
    4 hours ago










Your Answer





StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "65"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);













draft saved

draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f398551%2flogistic-function-with-a-slope-but-no-asymptotes%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown

























3 Answers
3






active

oldest

votes








3 Answers
3






active

oldest

votes









active

oldest

votes






active

oldest

votes









10












$begingroup$

Initially I was thinking you did want the horizontal asymptotes at $0$ still; I moved my original answer to the end. If you instead want $lim_xtopm infty f(x) = pminfty$ then would something like the inverse hyperbolic sine work?
$$
textasinh(x) = logleft(x + sqrt1 + x^2right)
$$



This is unbounded but grows like $log$ for large $|x|$ and looks like
asinh



I like this function a lot as a data transformation when I've got heavy tails but possibly zeros or negative values.



Another nice thing about this function is that $textasinh'(x) = frac1sqrt1+x^2$ so it has a nice simple derivative.




Original answer



$newcommandevarepsilon$Let $f : mathbb Rtomathbb R$ be our function and we'll assume
$$
lim_xtopm infty f(x) = 0.
$$



Suppose $f$ is continuous. Fix $e > 0$. From the asymptotes we have
$$
exists x_1 : x < x_1 implies |f(x)| < e
$$

and analogously there's an $x_2$ such that $x > x_2 implies |f(x)| < e$. Therefore outside of $[x_1,x_2]$ $f$ is within $(-e, e)$. And $[x_1,x_2]$ is a compact interval so by continuity $f$ is bounded on it.



This means that any such function can't be continuous. Would something like
$$
f(x) = begincases x^-1 & xneq 0 \ 0 & x = 0endcases
$$
work?






share|cite|improve this answer











$endgroup$








  • 1




    $begingroup$
    The "Related" threads include this unanswered question, in case anyone else has asked themselves the natural followup "what happens if you use asinh in a neural network?" stats.stackexchange.com/questions/359245/…
    $endgroup$
    – Sycorax
    yesterday











  • $begingroup$
    @Sycorax thanks, i was wondering about that
    $endgroup$
    – jld
    yesterday










  • $begingroup$
    My ears did indeed prick up. I have in the past found asinh() useful when you want to 'do log stuff' to both positive and negative numbers. It also gets around the quandry you can get in, where you need to do a log transform on data with zeros and have to judge an appropriate value of $a$ for $log(x + a)$
    $endgroup$
    – Ingolifs
    yesterday















10












$begingroup$

Initially I was thinking you did want the horizontal asymptotes at $0$ still; I moved my original answer to the end. If you instead want $lim_xtopm infty f(x) = pminfty$ then would something like the inverse hyperbolic sine work?
$$
textasinh(x) = logleft(x + sqrt1 + x^2right)
$$



This is unbounded but grows like $log$ for large $|x|$ and looks like
asinh



I like this function a lot as a data transformation when I've got heavy tails but possibly zeros or negative values.



Another nice thing about this function is that $textasinh'(x) = frac1sqrt1+x^2$ so it has a nice simple derivative.




Original answer



$newcommandevarepsilon$Let $f : mathbb Rtomathbb R$ be our function and we'll assume
$$
lim_xtopm infty f(x) = 0.
$$



Suppose $f$ is continuous. Fix $e > 0$. From the asymptotes we have
$$
exists x_1 : x < x_1 implies |f(x)| < e
$$

and analogously there's an $x_2$ such that $x > x_2 implies |f(x)| < e$. Therefore outside of $[x_1,x_2]$ $f$ is within $(-e, e)$. And $[x_1,x_2]$ is a compact interval so by continuity $f$ is bounded on it.



This means that any such function can't be continuous. Would something like
$$
f(x) = begincases x^-1 & xneq 0 \ 0 & x = 0endcases
$$
work?






share|cite|improve this answer











$endgroup$








  • 1




    $begingroup$
    The "Related" threads include this unanswered question, in case anyone else has asked themselves the natural followup "what happens if you use asinh in a neural network?" stats.stackexchange.com/questions/359245/…
    $endgroup$
    – Sycorax
    yesterday











  • $begingroup$
    @Sycorax thanks, i was wondering about that
    $endgroup$
    – jld
    yesterday










  • $begingroup$
    My ears did indeed prick up. I have in the past found asinh() useful when you want to 'do log stuff' to both positive and negative numbers. It also gets around the quandry you can get in, where you need to do a log transform on data with zeros and have to judge an appropriate value of $a$ for $log(x + a)$
    $endgroup$
    – Ingolifs
    yesterday













10












10








10





$begingroup$

Initially I was thinking you did want the horizontal asymptotes at $0$ still; I moved my original answer to the end. If you instead want $lim_xtopm infty f(x) = pminfty$ then would something like the inverse hyperbolic sine work?
$$
textasinh(x) = logleft(x + sqrt1 + x^2right)
$$



This is unbounded but grows like $log$ for large $|x|$ and looks like
asinh



I like this function a lot as a data transformation when I've got heavy tails but possibly zeros or negative values.



Another nice thing about this function is that $textasinh'(x) = frac1sqrt1+x^2$ so it has a nice simple derivative.




Original answer



$newcommandevarepsilon$Let $f : mathbb Rtomathbb R$ be our function and we'll assume
$$
lim_xtopm infty f(x) = 0.
$$



Suppose $f$ is continuous. Fix $e > 0$. From the asymptotes we have
$$
exists x_1 : x < x_1 implies |f(x)| < e
$$

and analogously there's an $x_2$ such that $x > x_2 implies |f(x)| < e$. Therefore outside of $[x_1,x_2]$ $f$ is within $(-e, e)$. And $[x_1,x_2]$ is a compact interval so by continuity $f$ is bounded on it.



This means that any such function can't be continuous. Would something like
$$
f(x) = begincases x^-1 & xneq 0 \ 0 & x = 0endcases
$$
work?






share|cite|improve this answer











$endgroup$



Initially I was thinking you did want the horizontal asymptotes at $0$ still; I moved my original answer to the end. If you instead want $lim_xtopm infty f(x) = pminfty$ then would something like the inverse hyperbolic sine work?
$$
textasinh(x) = logleft(x + sqrt1 + x^2right)
$$



This is unbounded but grows like $log$ for large $|x|$ and looks like
asinh



I like this function a lot as a data transformation when I've got heavy tails but possibly zeros or negative values.



Another nice thing about this function is that $textasinh'(x) = frac1sqrt1+x^2$ so it has a nice simple derivative.




Original answer



$newcommandevarepsilon$Let $f : mathbb Rtomathbb R$ be our function and we'll assume
$$
lim_xtopm infty f(x) = 0.
$$



Suppose $f$ is continuous. Fix $e > 0$. From the asymptotes we have
$$
exists x_1 : x < x_1 implies |f(x)| < e
$$

and analogously there's an $x_2$ such that $x > x_2 implies |f(x)| < e$. Therefore outside of $[x_1,x_2]$ $f$ is within $(-e, e)$. And $[x_1,x_2]$ is a compact interval so by continuity $f$ is bounded on it.



This means that any such function can't be continuous. Would something like
$$
f(x) = begincases x^-1 & xneq 0 \ 0 & x = 0endcases
$$
work?







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited yesterday

























answered yesterday









jldjld

12.3k23353




12.3k23353







  • 1




    $begingroup$
    The "Related" threads include this unanswered question, in case anyone else has asked themselves the natural followup "what happens if you use asinh in a neural network?" stats.stackexchange.com/questions/359245/…
    $endgroup$
    – Sycorax
    yesterday











  • $begingroup$
    @Sycorax thanks, i was wondering about that
    $endgroup$
    – jld
    yesterday










  • $begingroup$
    My ears did indeed prick up. I have in the past found asinh() useful when you want to 'do log stuff' to both positive and negative numbers. It also gets around the quandry you can get in, where you need to do a log transform on data with zeros and have to judge an appropriate value of $a$ for $log(x + a)$
    $endgroup$
    – Ingolifs
    yesterday












  • 1




    $begingroup$
    The "Related" threads include this unanswered question, in case anyone else has asked themselves the natural followup "what happens if you use asinh in a neural network?" stats.stackexchange.com/questions/359245/…
    $endgroup$
    – Sycorax
    yesterday











  • $begingroup$
    @Sycorax thanks, i was wondering about that
    $endgroup$
    – jld
    yesterday










  • $begingroup$
    My ears did indeed prick up. I have in the past found asinh() useful when you want to 'do log stuff' to both positive and negative numbers. It also gets around the quandry you can get in, where you need to do a log transform on data with zeros and have to judge an appropriate value of $a$ for $log(x + a)$
    $endgroup$
    – Ingolifs
    yesterday







1




1




$begingroup$
The "Related" threads include this unanswered question, in case anyone else has asked themselves the natural followup "what happens if you use asinh in a neural network?" stats.stackexchange.com/questions/359245/…
$endgroup$
– Sycorax
yesterday





$begingroup$
The "Related" threads include this unanswered question, in case anyone else has asked themselves the natural followup "what happens if you use asinh in a neural network?" stats.stackexchange.com/questions/359245/…
$endgroup$
– Sycorax
yesterday













$begingroup$
@Sycorax thanks, i was wondering about that
$endgroup$
– jld
yesterday




$begingroup$
@Sycorax thanks, i was wondering about that
$endgroup$
– jld
yesterday












$begingroup$
My ears did indeed prick up. I have in the past found asinh() useful when you want to 'do log stuff' to both positive and negative numbers. It also gets around the quandry you can get in, where you need to do a log transform on data with zeros and have to judge an appropriate value of $a$ for $log(x + a)$
$endgroup$
– Ingolifs
yesterday




$begingroup$
My ears did indeed prick up. I have in the past found asinh() useful when you want to 'do log stuff' to both positive and negative numbers. It also gets around the quandry you can get in, where you need to do a log transform on data with zeros and have to judge an appropriate value of $a$ for $log(x + a)$
$endgroup$
– Ingolifs
yesterday













9












$begingroup$

You could just add a term to a logistic function:



$$
f(x; a, b, c, d, e)=fraca1+bexp(-cx) + dx + e
$$



The asymptotes will have slopes $d$.



Here is an example with $a=10, b = 1, c = 2, d = frac120, e = -5$:



Sigmoid






share|cite|improve this answer









$endgroup$








  • 1




    $begingroup$
    I think this answer is the best because if you zoom out far enough it's just a straight line with a little wiggle in the middle. Gives the most intuitive behavior at large x but retains the sigmoid shape.
    $endgroup$
    – user1717828
    yesterday















9












$begingroup$

You could just add a term to a logistic function:



$$
f(x; a, b, c, d, e)=fraca1+bexp(-cx) + dx + e
$$



The asymptotes will have slopes $d$.



Here is an example with $a=10, b = 1, c = 2, d = frac120, e = -5$:



Sigmoid






share|cite|improve this answer









$endgroup$








  • 1




    $begingroup$
    I think this answer is the best because if you zoom out far enough it's just a straight line with a little wiggle in the middle. Gives the most intuitive behavior at large x but retains the sigmoid shape.
    $endgroup$
    – user1717828
    yesterday













9












9








9





$begingroup$

You could just add a term to a logistic function:



$$
f(x; a, b, c, d, e)=fraca1+bexp(-cx) + dx + e
$$



The asymptotes will have slopes $d$.



Here is an example with $a=10, b = 1, c = 2, d = frac120, e = -5$:



Sigmoid






share|cite|improve this answer









$endgroup$



You could just add a term to a logistic function:



$$
f(x; a, b, c, d, e)=fraca1+bexp(-cx) + dx + e
$$



The asymptotes will have slopes $d$.



Here is an example with $a=10, b = 1, c = 2, d = frac120, e = -5$:



Sigmoid







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered yesterday









COOLSerdashCOOLSerdash

16.5k75293




16.5k75293







  • 1




    $begingroup$
    I think this answer is the best because if you zoom out far enough it's just a straight line with a little wiggle in the middle. Gives the most intuitive behavior at large x but retains the sigmoid shape.
    $endgroup$
    – user1717828
    yesterday












  • 1




    $begingroup$
    I think this answer is the best because if you zoom out far enough it's just a straight line with a little wiggle in the middle. Gives the most intuitive behavior at large x but retains the sigmoid shape.
    $endgroup$
    – user1717828
    yesterday







1




1




$begingroup$
I think this answer is the best because if you zoom out far enough it's just a straight line with a little wiggle in the middle. Gives the most intuitive behavior at large x but retains the sigmoid shape.
$endgroup$
– user1717828
yesterday




$begingroup$
I think this answer is the best because if you zoom out far enough it's just a straight line with a little wiggle in the middle. Gives the most intuitive behavior at large x but retains the sigmoid shape.
$endgroup$
– user1717828
yesterday











5












$begingroup$

I will go ahead and turn the comment into an answer. I suggest
$$
f(x) = operatornamesign(x)logright),
$$

which has slope tending towards zero, but is unbounded.



edit by popular demand, a plot, for $|x|le 30$:
enter image description here






share|cite|improve this answer











$endgroup$








  • 2




    $begingroup$
    a graph of the function would be useful
    $endgroup$
    – qwr
    18 hours ago










  • $begingroup$
    @qwr and done...
    $endgroup$
    – steveo'america
    4 hours ago















5












$begingroup$

I will go ahead and turn the comment into an answer. I suggest
$$
f(x) = operatornamesign(x)logright),
$$

which has slope tending towards zero, but is unbounded.



edit by popular demand, a plot, for $|x|le 30$:
enter image description here






share|cite|improve this answer











$endgroup$








  • 2




    $begingroup$
    a graph of the function would be useful
    $endgroup$
    – qwr
    18 hours ago










  • $begingroup$
    @qwr and done...
    $endgroup$
    – steveo'america
    4 hours ago













5












5








5





$begingroup$

I will go ahead and turn the comment into an answer. I suggest
$$
f(x) = operatornamesign(x)logright),
$$

which has slope tending towards zero, but is unbounded.



edit by popular demand, a plot, for $|x|le 30$:
enter image description here






share|cite|improve this answer











$endgroup$



I will go ahead and turn the comment into an answer. I suggest
$$
f(x) = operatornamesign(x)logright),
$$

which has slope tending towards zero, but is unbounded.



edit by popular demand, a plot, for $|x|le 30$:
enter image description here







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited 4 hours ago

























answered yesterday









steveo'americasteveo'america

23319




23319







  • 2




    $begingroup$
    a graph of the function would be useful
    $endgroup$
    – qwr
    18 hours ago










  • $begingroup$
    @qwr and done...
    $endgroup$
    – steveo'america
    4 hours ago












  • 2




    $begingroup$
    a graph of the function would be useful
    $endgroup$
    – qwr
    18 hours ago










  • $begingroup$
    @qwr and done...
    $endgroup$
    – steveo'america
    4 hours ago







2




2




$begingroup$
a graph of the function would be useful
$endgroup$
– qwr
18 hours ago




$begingroup$
a graph of the function would be useful
$endgroup$
– qwr
18 hours ago












$begingroup$
@qwr and done...
$endgroup$
– steveo'america
4 hours ago




$begingroup$
@qwr and done...
$endgroup$
– steveo'america
4 hours ago

















draft saved

draft discarded
















































Thanks for contributing an answer to Cross Validated!


  • Please be sure to answer the question. Provide details and share your research!

But avoid


  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f398551%2flogistic-function-with-a-slope-but-no-asymptotes%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







Popular posts from this blog

Sum ergo cogito? 1 nng

三茅街道4182Guuntc Dn precexpngmageondP