Simple statistical moment question

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Discussion Overview

The discussion revolves around the relevance of calculating skewness and kurtosis for a sample when a probability density function (pdf) is already available. Participants explore the implications of these statistical moments in relation to the shape of the pdf and their potential utility in data analysis.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions the necessity of calculating skewness and kurtosis if a pdf is already known, suggesting that these moments may only reflect the shape of the pdf.
  • Another participant highlights the ambiguity of terms like "mean," "variance," "skewness," and "kurtosis," noting that each has multiple interpretations that could affect their application.
  • A participant expresses uncertainty about the value of computing statistical moments, acknowledging that while they provide insights into the pdf's shape, visual representations can be misleading.
  • It is suggested that calculating skewness and kurtosis could allow for quantitative comparisons between different pdfs, providing a clearer understanding of their characteristics.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether calculating skewness and kurtosis is necessary when a pdf is available. Multiple viewpoints are presented regarding the utility and interpretation of these statistical moments.

Contextual Notes

Participants note the ambiguity in statistical terminology and the potential for misleading graphical representations, which may impact the interpretation of skewness and kurtosis.

member 428835
hi pf!

so i am going to take the skewness and kurtosis of a sample. however, if i already have a pdf, is there really any reason for doing this?

thanks!

josh
 
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Well, you are the one who is going to do it, you tell me?
 
joshmccraney said:
so i am going to take the skewness and kurtosis of a sample

Terms like "mean", "variance", "skewness" are ambiguous. Each such term has at least 3 possible meanings. For example, "variance" can mean "the variance of a random variable", which is a property of the pdf of the random variable. "Vaiance" can also mean the "variance of a sample". "Variance" can also mean "an estimator of the variance of the random variable" - this need not be the same as "the variance of a sample".
 
Simon Bridge said:
Well, you are the one who is going to do it, you tell me?
well, I'm really not sure. i mean, a part of me thinks if we have the pdf, all the skewness and kurtosis are going to tell me is the pdf shape. skewness tells if one tail is longer than the other. kurtosis talks about flatness and tail thickness.

but on the other hand, graphs can be misleading, and we can't always trust what we see, so maybe I should compute these statistical moments?

what do you think?
 
Depends what you want the data to tell you.
You'd normally want a measure for the different features like that so that you can compare one pdf to another quantitatively... like you can say that one graph is 15% more skewed to the left than the other or something.

So if you know what you got the pdf for in the first place, what you want to do with it, then you will know if you need the other stuff.
 

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