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I am given a data set of velocity($u$) & time ($t$). And Asked to calculate the pdf.

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I have computed the pdf from the given data after coding it on Matlab. And fitted a $10$th order polynomial.

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According to the second problem, I'm supposed to evaluate mean,rms, skewness and kurtosis. So do I have to use this fitted curve of pdf as a function of u and calculate these quantities by integration? As they are defined.

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The above is the method, I've been taught by the professor.

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  • $\begingroup$ Why do you fit your data with a polynomial ? It is visibly to be fitted with a gaussian (skewness 0, kurtosis 3). $\endgroup$
    – Jean Marie
    Feb 8, 2019 at 19:28
  • $\begingroup$ I have not been taught about this in the course. I can calculate skewness after integrating the pdf ( function of u ) as third moment. $\endgroup$
    – Anshuman Sinha
    Feb 8, 2019 at 19:31
  • $\begingroup$ It is strange that your instructor hasn't mentionned the Gauss (or "normal") distribution. Besides, as long as you do all your calculations say between 2 and 4, why not a polynomia ? But have you tried to extend the representation of your polynomial say on [-5, 10] : have you seen the behavior of your "approximation" polynomial ? $\endgroup$
    – Jean Marie
    Feb 8, 2019 at 19:37
  • $\begingroup$ he's not a good teacher. I'm adding a picture of what I know about calculating 3rd and 4th moment. $\endgroup$
    – Anshuman Sinha
    Feb 8, 2019 at 19:46
  • $\begingroup$ Evaluation of the mean $m$ and experimental variance by "mean" and "var" is immediate with Matlab (on initial data, no need of approximation). After that, I imagine that you have to use "integral(p(x).*(x-m).^3,2,4)". The result, as I said shouldn't be far from 0. The same with exponent 4. $\endgroup$
    – Jean Marie
    Feb 8, 2019 at 20:02

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