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Math Help - Normal distribution Interpretation Algorithm

  1. #1
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    Normal distribution Interpretation Algorithm

    Hi all, in a program I have to generate a random number using the Normal distribution, the algorithm found online, but I'd like to help us understand complemtamente the theoretical foundation behind it: Let's see:

    The random number is generated by a normal distribution, which receives the parameters \mu and \sigma, in my case \mu = 80, and \sigma = 15. The code is as follows:

    Function xNORMAL(mu, sigma)
    Dim NORMAL01
    Const Pi As Double = 3.14159265358979
    Randomize
    NORMAL01 = Sqr((-2 * LN(Rnd))) * Sin(2 * Pi * Rnd)
    xNORMAL = mu + sigma * NORMAL01
    End Function
    Function LN(x)
    LN = Log(x) / Log(Exp(1))
    End Function
    In this part: xNORMAL = mu + sigma * NORMAL01, I understand that what they do is to clear the typing X given by:
    <br />
Z = \displaystyle\frac{X- \mu}{\sigma}

    But I have no clear rationale behind this calculation:

    I guess it is to find the value of the random variable on an integration of the density function that appears in this link:

    Normal distribution - Wikipedia, the free encyclopedia

    Whose limits in this case would be Ln (Rnd), is this how I think?

    But why the function is expressed in terms of Sin (x)?. Perhaps using Fourier transform?


    Thank you if you help me solve these questions.


    A greeting.

    Dogod.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Dogod11 View Post
    Hi all, in a program I have to generate a random number using the Normal distribution, the algorithm found online, but I'd like to help us understand complemtamente the theoretical foundation behind it: Let's see:

    The random number is generated by a normal distribution, which receives the parameters \mu and \sigma, in my case \mu = 80, and \sigma = 15. The code is as follows:

    In this part: xNORMAL = mu + sigma * NORMAL01, I understand that what they do is to clear the typing X given by:
    <br />
Z = \displaystyle\frac{X- \mu}{\sigma}

    But I have no clear rationale behind this calculation:

    I guess it is to find the value of the random variable on an integration of the density function that appears in this link:

    Normal distribution - Wikipedia, the free encyclopedia

    Whose limits in this case would be Ln (Rnd), is this how I think?

    But why the function is expressed in terms of Sin (x)?. Perhaps using Fourier transform?


    Thank you if you help me solve these questions.


    A greeting.

    Dogod.
    Google "Box Muller"

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
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    Thanks.
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