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I want to calculate Gauss-Hermite moments, such as h1,h2, h3, h4 moments from the values in an array of numbers which represent velocity distribution of stars in a galaxy. How would I fit a curve to these values that would be a Gauss-Hermite curve fitting and get the value of h1, h2, h3 and h4 using Python? For example, if I want to find standard deviation or mean of an array in python I can simply use np.std or np.mean. Is there any similar functions for Gauss-Hermite?

Please also share links or articles if relevant. Feel free to ask me if anything is unclear in my question. Thanks a lot!

EDIT: I found a post by MIchele Scipioni at https://mscipio.github.io/post/fitting-functions-to-data/ which is doing something similar to what I am looking for but in a more complicated manner. I just want to be ale to fit the Gauss-Hermite polynomial of the following form [also presented in the post I have linked] to an array of data and be able to generate initial guesses for the input parameters automatically and get output fitted values for skewness and kurtosis : enter image description here

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    $\begingroup$ You checked numpy.org/doc/stable/reference/… ? $\endgroup$
    – planetmaker
    Jan 18, 2022 at 18:30
  • $\begingroup$ @planetmaker, yes I did check the functions and examples on that reference page but I am not sure which function there can directly give the moments h1,h2,h3,4. Do you have any idea? $\endgroup$
    – Jerome
    Jan 19, 2022 at 6:36
  • $\begingroup$ @planetmaker, could we use numpy.polynomial.hermite.hermfit? but honestly I think it would be better if we could define the gauss-hermite polynomial ourselves. $\endgroup$
    – Jerome
    Jan 19, 2022 at 6:54

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