Simple statistical moment question

[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

 

[Simon Bridge]

Well, you are the one who is going to do it, you tell me?

 

[Stephen Tashi]

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".

 

[member 428835]

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?

 

[Simon Bridge]

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.