Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

PDF of a sine wave cycle

  1. Jan 16, 2009 #1
    Does anybody know what the pdf of a sine wave cycle is? Or perhaps how to derive it? The problem can be done numerically, but surely there is an analytic expression for this function? There is a numerical solution available at http://www.forexmt4.com/_MT4_Systems/Fisher - The Collection/2775-fisher-130fish.pdf, figure 2.

    Thanks,

    Natski
     
  2. jcsd
  3. Jan 18, 2009 #2

    ssd

    User Avatar

    Pls clarify which is the rv.
     
  4. Jan 19, 2009 #3
    Hi ssd. Note sure what you mean by the rv.

    Actually I have now solved this problem. The pdf of a sine wave is given by:

    \begin{equation}
    \textrm{P}(x) \textrm{ d}x= \frac{1}{\pi \sqrt{1-x^2}} \textrm{ d}x
    \end{equation}

    Cheers,
    Natski
     
  5. Jan 21, 2009 #4

    ssd

    User Avatar

    R.V. is "random variable".
     
  6. Apr 20, 2010 #5
    Could you show the derivation?

    Hmmm... From http://en.wikipedia.org/wiki/Differ...ns#Differentiating_the_inverse_sine_function":

    [tex]\frac{d}{dx} \arcsin x & {}= \frac{1}{\sqrt{1-x^2}}\\[/tex]
     
    Last edited by a moderator: Apr 25, 2017 at 8:26 AM
  7. May 5, 2010 #6
    Actually that makes sense. As the slope of the function increases, the likelihood of getting a point at that value increases, so it would seem that the PDF of a function is the derivative of the http://en.wikipedia.org/wiki/Inverse_function" to figure it out, like using only a single cycle of the sine wave, which is what arcsin does.

    So for [tex]y = x^2[/tex], for instance, the inverse function is [tex]x = \pm\sqrt{y}[/tex], and the derivative of one side of this (since both positive and negative are identical) is [tex]1 \over {2 \sqrt{x}}[/tex]. Weight it so that the total area under the curve is 1, and it's the PDF.

    But what about functions that don't have inverses, and also aren't symmetrical or repetitious? They still have PDFs. Do you just break them up into piecewise functions at each http://en.wikipedia.org/wiki/Stationary_point", and then sum them)
     
    Last edited by a moderator: Apr 25, 2017 at 8:48 AM
  8. May 6, 2010 #7

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Yes, I think you would have to do it that way.
     
    Last edited by a moderator: Apr 25, 2017 at 8:50 AM
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: PDF of a sine wave cycle
  1. Compare PDF (Replies: 1)

  2. Finding the PDF? (Replies: 1)

  3. Cdf and pdf (Replies: 4)

Loading...