Kurtosis
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- čas přidán 22. 08. 2024
- This video introduces the concept of kurtosis of a random variable, and provides some intuition behind its mathematical foundations. Check out ben-lambert.co... for course materials, and information regarding updates on each of the courses. Quite excitingly (for me at least), I am about to publish a whole series of new videos on Bayesian statistics on youtube. See here for information: ben-lambert.co... Accompanying this series, there will be a book: www.amazon.co....
Im taking financial econometrics now and I am often lost in class. Thank you for uploading an entire course that allows students to take things step by step-I find your videos very helpful. Much appreciated.
Thanks for posting. This couldn't be explained any simpler
This is what is called "explaining"! Thank you!
Fantastic video; very well explained. Thank you!
I thought this was a diet.
Really well explained, thank you greatly for your videos!
you such alani
Thanks, Ben
Looks to me as if the variance of the yellow distribution was definitely smaller.. Anyway thanks a lot for your videos!
I agree that the variances appear to be different. How can they be the same?
yitzweb he drew 2 different looking density curves. It's possible to have same variance but different kurtosis. Because one could be more spread out in the center and have shorter tails and one could be thinner in the middle and have slightly wider tails. The simple drawings weren't the best, but is a possible scenario
exactly what I needed.
Great video, quick and simple, thank you very much!
Great insight…
What do we do with excess kurtosis - how do we accommodate it, when does it invalidate our tests?
Excellent. Thanks for the video
Thanks. It really helped
but surely the variance (or second central moment) still tells us something about the tails ? Because calculating the variance still involves squaring the difference between even extreme values of X. I grant you that the fourth central moment would pronounce extreme values more greatly, but its not as if these extreme values are ignored when calculating variance? I hope I'm making sense....
Hi, thanks for your message. Yes, you are right - of course the 2nd moment does tell us about the tails. However, due to the density of the points in the shoulders, it ends up giving more weight to those points, on average. What I really meant in this video is that the 2nd moment gives less weight to the tails relative to a fourth moment; it's all relative. Hope that makes some sense. Best, Ben
Yes that does make perfect sense. I guess you could even use higher ordered moments to accentuate more greatly the relative size of the tails! Why stop at the fourth moment...anyway thanks for your videos!
Hello Adrian, can you explained to me further, I don't understand
but.. isnt kurtosis equal to the 4th moment about the mean?? ay 4:11
Thank you. I owe you my job
Just to clarify, lowercase sigma is Standard deviation, right?
Yes. Best, Ben
Good job brother.
Just wanted to ask how can I get a result of leptokurtic Distribution?
Thank you.
Your illustrations are wrong. Those two distributions *do not* have the same variance.
The higher kurtosis / fatter-tailed distribution should have the higher/thinner peak to make up for the variance of the outliers.
how to get the s in kurtosis
How do I apply this in research?
What do u mean by pdf'
nice
Bouncer gaya after 4:00
I decided to write a comment because I thought that perhaps some others are hung up on the same issue that I am. Then again, my hangup is due to lazy thinking, and probably most listeners to these videos are smarter than I am.
I look at the formula for kurtosis and I see that the numerator looks very much like the square of the variance. The denominator is, in fact, the square of the variance, though it is written as the fourth power of sigma, whatever the heck sigma is. So aren’t we just dividing the square of the variance by itself?
If I think about it with more effort I realize that the numerator is the fourth power of each of the differences, which is then summed and divided by N. Variance is the second power of each of the differences, which is then summed and divided by N, which in this case is then squared. These two operations give very different results.
Unfortunately the notation implies that we are taking the fourth power of sigma to compute the denominator. This is misleading. Sigma, you all know, is the standard deviation. It is the square root of the variance, and it cannot be computed, as far as I know, without first computing the variance. Alas we use the notation sigma squared to refer to the variance, but this is not because we compute it based on a sum of squares, but because someone decided to name the variance after its progeny, I think. Why do we do that? I thought math was supposed to be rational.
Btw, Ben, the videos are great! Thanks a ton.
what is M4? it says kurtosis is M4 at the top of the slide, but then you said kurtosis is gamma which is = to M4/sd^4. Also why are we using the power of 4? surely a higher number will put more weighting on the tails, so why not ^400? I dont really get it, seems arbitary.
Good. Nothing about "peakedness." Kurtosis has nothing to do with "peakedness."
test
test 2
test 3
I dont understand the single word that you are telling and you dont know how to teach student..
horrible writing
how to get the s in kurtosis
+Aly Villegas square root of Variance