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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.
 one year ago
 one year 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.
 one year ago
 one year ago

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datanewbBest ResponseYou've already chosen the best response.0
In 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.
 one year ago

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

datanewbBest ResponseYou've already chosen the best response.0
Sorry, 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
 one year ago

datanewbBest ResponseYou've already chosen the best response.0
yes, it is a double power
 one year ago

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

datanewbBest ResponseYou've already chosen the best response.0
Changing 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.
 one year ago

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

datanewbBest ResponseYou've already chosen the best response.0
@frx, exactly. That is a clearer explanation of what I'm trying to do.
 one year ago

frxBest ResponseYou've already chosen the best response.1
Hmm 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
 one year ago

datanewbBest ResponseYou've already chosen the best response.0
unfortunately, 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:\[2^{\left(\left(\frac{x}{8}\right)^{2}\right)}\]
 one year ago

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

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

datanewbBest ResponseYou've already chosen the best response.0
oh, 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
 one year ago

datanewbBest ResponseYou've already chosen the best response.0
http://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.
 one year ago
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