Our group, along with a few students, has been reading statistics handbook and refreshing our understanding of the basic statistics. Some time ago, I was given to cover a chapter about the central limit theorem, which reminded me that I had already given a similar presentation while being PhD student myself. While diving into the topic, I have noticed a couple things, which are usually glanced over in a typical statistics handbook. Let me share them with you.

This time we explore infinite divisibility. Our previous mathematical explorations of the stable distributions topic have relied on this property, because it simplifies many of the analytical derivations. But there are distributions, which are infinitely divisible but not stable. This time let us take a look at sums of Gamma distributed random variates.

Over the last few posts we have taken a look at the Cauchy distribution, which apparently has undefined mean and variance. You will find a useful review and some novel personal insights from an enthusiastic student Ananya Chadha in the video below.

If you are interested in complex systems, physical modeling of opinion dynamics or financial markets, then you might be interested in my invitation to host MSCA postdoctoral fellows.

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Our group, along with a few students, has been reading statistics handbook and refreshing our understanding of the basic statistics. I was given to cover a chapter about the central limit theorem, which reminded me that I had already given a similar presentation while being PhD student myself. While diving into the topic, I have noticed a couple things, which are usually glanced over in a typical statistics handbook. Let me share them with you.

In the previous post we have taken a look at a distribution whose mean and variance are undefined. We know that the central limit theorem holds only if mean and variance of the sample distribution are defined and finite. So what happens if we sum Cauchy random variates?

Our group, along with a few students, has been reading statistics handbook and refreshing our understanding of the basic statistics. I was given to cover a chapter about the central limit theorem, which reminded me that I had already given a similar presentation while being PhD student myself. While diving into the topic, I have noticed a couple things, which are usually glanced over in a typical statistics handbook. Let me share them with you.

In the previous post we have talked about a peculiar result in statistics - that an average of well-behaved random variates (those that come from distributions with finite mean and variance) is distributed according to the normal (Gaussian) distribution. But what happens if the variates are not well-behaved? Accompanying video briefly mentions Cauchy distribution, as a distribution describing random variates, which are not well-behaved. Let us take a look at it!