Area under Gaussian Distribution Curve = 1 Problem

FredFripp

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Jul 30, 2020
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I am writing a music program in which I need to determine amplitude levels by solving for y=f(x) for every whole integer x between 1 and some arbitrary value between say 20 and 300. I need the area under the curve to be equal to one or some reasonable approximation. I took bunches of cal in high school and college but i have forgotten most of it. Can you help?
 

LCKurtz

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I am writing a music program in which I need to determine amplitude levels by solving for y=f(x) for every whole integer x between 1 and some arbitrary value between say 20 and 300. I need the area under the curve to be equal to one or some reasonable approximation. I took bunches of cal in high school and college but i have forgotten most of it. Can you help?
It would be helpful if you would give more information about what you are doing. You talk about amplitude levels and solving \(\displaystyle y=f(x)\) and then in the title you mention the Gaussian distribution. Are you talking about the standard normal distribution \(\displaystyle f(x) = \frac 1 {\sqrt{2\pi}}e^{-\frac {x^2} 2}\)? Are you just wanting to evaluate that for various values of \(\displaystyle x\)? Do the \(\displaystyle y\) values represent amplitudes? More info please.
 

FredFripp

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Okay I have done some more work on this today and I guess I should rephrase my question: I am trying to write an equation which will give me a non-normal distribution curve (i thought it was possible to use the standard normal distribution equation as you described above, and yes that is what I have programmed into my work) between two points that is skewed, leptokurtic, platykurtic, and centered around a mean which I can control. I will be able to provide inputs for mu, theta, bounding points, etc with a midi controller (like the knobs djs use). I have programmed an interface so far in which I can transform the normal distribution around a mu value which I input but the problem is that the entire bell curve is moved intact. I would like to skew the graph while maintaining limits between the bounding values. If I can keep an area under the curve of 1 that would also rule. I read today that the square in the exponent of e is what creates symmetry around mu, so I am about to get to work on changing that as my input variable to see the results but I am sure it will probably give me some odd result. Ha. I don't know what Im doing!

Thanks for the response.

jmm

edit To answer all questions directly:

I was talking about normal distro, not anymore
I do want to evaluate the equation for various values of x to determine y which are amplitude levels.
 

LCKurtz

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This isn't really an area I am highly qualified in. I think you are looking for skewed distributions. Two examples that come to mind that you might consider are beta and lognormal distributions. Look them up and see if they are any help to you. An advantage of using probability distributions is they automatically have total area equal \(\displaystyle 1\).
 

FredFripp

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Great. Thanks you so much. I have had a huge problem finding any equations to give me this sort of graph. Most everything I have found dealing with statistics just have functions to normalize skewed graphs to normal distribution which is what I don't want. Ill check it out. Thanks for the advice.
 
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