I've learnt that for parametrical distributions you can describe the family of statistical model with the parameters, one such example has been the uniform distribution. I just came across a text saying that the uniform distribution is "inherently non-parametric". What is really the difference between parametric and non-parametric distributions?

(I have already read the previous answers on this topic).

edit: link https://en.wikipedia.org/wiki/Discrete_uniform_distribution

I don't have a background in statistics/mathematics/machine learning.

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    $\begingroup$ Can you please reference/link that text? $\endgroup$ Oct 27, 2020 at 12:01
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    $\begingroup$ Please link those previous answers so we have a baseline of what you know. // Where did you read the comment about uniform distributions? $\endgroup$
    – Dave
    Oct 27, 2020 at 12:01
  • $\begingroup$ Maybe one way to start looking at this is the difference between distributions that you know the data follows and have a density which is parameterized by a vector $\theta \in \mathbb{R}^n$, $p_\theta(x) = p(x \Vert \theta)$ and models where you can not assume any prior knowledge of the distribution (you can find this under non-parametric density estimation). Maybe this could be a good heads up for you. In this sense the uniform distribution is parameterized though, i.e. by the volume of the set which the distribution is defined on $\lambda(A), A\subset\mathbb{R}^n$, $\lambda$ Lebesguemeasure. $\endgroup$
    – Abbraxas
    Oct 27, 2020 at 12:06
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    $\begingroup$ Does this answer your question? Why would parametric statistics ever be preferred over nonparametric? $\endgroup$ Oct 27, 2020 at 13:36
  • $\begingroup$ @Dave, I found a statement to this effect by Googling. It goes to an awful blog full of misinformation and complete nonsense. $\endgroup$
    – whuber
    Oct 27, 2020 at 15:50


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