A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
Trying to adjust this equation so that it will have fatter tails?\[3^{\left(\frac{x}{6}\right)^{2}} \] Any ideas? It is similar to the probability distribution function.
 2 years ago
Trying to adjust this equation so that it will have fatter tails?\[3^{\left(\frac{x}{6}\right)^{2}} \] Any ideas? It is similar to the probability distribution function.

This Question is Closed

datanewb
 2 years ago
Best ResponseYou've already chosen the best response.0In the attached image, the black line is the graph of \[ 3^{\left(\frac{x}{6}\right)^{2}}\] and the red line is what I'd like to find an equation for.

frx
 2 years ago
Best ResponseYou've already chosen the best response.1Can't be the right equation: http://www.wolframalpha.com/input/?i=3%28x%2F6%29^2

datanewb
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry, this page did not translate my latex correctly, here is the equation I was trying http://www.wolframalpha.com/input/?i=3%5E%28%28x%2F6%29%5E2%29

datanewb
 2 years ago
Best ResponseYou've already chosen the best response.0yes, it is a double power

datanewb
 2 years ago
Best ResponseYou've already chosen the best response.0Does this make it clearer? \[3^{\left(\left(\frac{x}{6}\right)^{2}\right)}\]

datanewb
 2 years ago
Best ResponseYou've already chosen the best response.0Changing the 6 to say 12 results in a wider "distribution", but the entire the is wider. I'm trying to keep the top narrow and the bottom wide.

frx
 2 years ago
Best ResponseYou've already chosen the best response.1So you want the decay to take longer time to asymptote 0 and also start the decay a little earlier?

datanewb
 2 years ago
Best ResponseYou've already chosen the best response.0@frx, exactly. That is a clearer explanation of what I'm trying to do.

frx
 2 years ago
Best ResponseYou've already chosen the best response.1Hmm this was a bit tricky, not right but on the right way http://www.wolframalpha.com/input/?i=2^%28%28x%2F8%29^2%29+from+0+to+20

datanewb
 2 years ago
Best ResponseYou've already chosen the best response.0unfortunately, I think you've just made the entire distribution wider. In the attached image, f(x) is the original function \[3^{\left(\left(\frac{x}{6}\right)^{2}\right)}\], and g(x) is the new one:\[2^{\left(\left(\frac{x}{8}\right)^{2}\right)}\]

datanewb
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry, I'm equally unfamiliar with gnuplot and wolfram alpha, I guess I should just stick with one. :)

frx
 2 years ago
Best ResponseYou've already chosen the best response.1Hmm just an idea, what if you choose a couple of x and y values and construct the function backwards?

datanewb
 2 years ago
Best ResponseYou've already chosen the best response.0oh, that's a cool idea. I'll try that on wolfram... my current line of thinking had been to add multiple functions together. I know to make the top fatter, you can add to slightly shifted distribution functions

datanewb
 2 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=sextic+fit+100%2C96%2C88%2C75%2C61%2C46%2C35%2C35%2C17%2C12%2C8%2C5%2C3%2C2%2C1.5%2C1.2%2C.9%2C.8%2C.7%2C.6 Well, this works pretty well. I was hoping there would be a better method than brute force, some deductive way of figuring it out, but I'm happy to have found a function that I can use. Thanks.
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.