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    moments vs parameters




    Hi there,

    could you help me to understand the difference between moments and parameters of a distribution?
    I read definitions of moments like quantitative measures describing the shape of a set of points but this is also what the parameters of a given distribution do.

    Thanks for that!
    Best
    Ilaria

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    Re: moments vs parameters

    Quote Originally Posted by ilaria View Post
    Hi there,

    could you help me to understand the difference between moments and parameters of a distribution?
    I read definitions of moments like quantitative measures describing the shape of a set of points but this is also what the parameters of a given distribution do.
    What distributions do you know? You might be tripped up since for the normal distribution the two parameters we typically use also coincide with the moments of the distribution. This is not the case for a lot of distributions.
    I don't have emotions and sometimes that makes me very sad.

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    Re: moments vs parameters

    Quote Originally Posted by Dason View Post
    What distributions do you know? You might be tripped up since for the normal distribution the two parameters we typically use also coincide with the moments of the distribution. This is not the case for a lot of distributions.
    Thanks. So what is the theoretical difference between moments and parameters? Are the moments of a distribution (independently from the parameters that describe it) always mean and SD of that distribution?

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    Re: moments vs parameters


    "Moment" and "Parameter" itself has its own, unique and clear definition and you can find them out very easily on the web.

    "Moment" of a random variable / distribution is the expectation of a polynomial of the random variable (depends on what kind of moment)

    A parametric distribution is a family of distributions which can be uniquely characterized once the parameter is fixed. And as usual it can always be re-parametrized - like you can write a (distribution) function in terms of different arguments. So you can always use moment(s) to parametrize a distribution, like the normal distribution; on the other hand you can also use different parametrization, like using the reciprocal of SD to parametrize normal distribution, which is known to be the precision parameter.

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