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Is it possible to have infinite variance?
Models with infinite variance have right tails that extend to infinity. Variance is a measure of how spread out a distribution is. Distributions with infinite variance have fat upper tails that decrease at an extremely slow rate. The dataset’s empirical distribution function appears to decline like a power law.
Can expectations be infinite?
It is not surprising that the expected value is infinite when infinity is a possible value. However, the expected value can be infinite, even if the random variable is finite-valued. Let’s look at an example.
What’s the difference between infinite variance and finite variance?
The infinite variance means that random values don’t tend to concentrate around the mean too tightly. It could mean that there’s large enough probability that the next random number will be very far away from the mean. The distributions like Normal (Gaussian) can produce random numbers very far away from the mean,…
When does infinite variance occur in a population?
Infinite variance happens when the integral (sum) defining the population variance increases beyond any finite bound as the limit is taken. Some discussion of examples here – Glen_b -Reinstate Monica Apr 20 ’14 at 1:31
Is the heavy tailed the same as infinite variance?
$\\begingroup$No, heavy-tailedis not the same as having infinite variance, or at least, not in my view. However, I am not a statistician and so you should wait for for a more authoritative answer from highly-ranked users in this forum.$\\endgroup$– Dilip SarwateApr 19 ’14 at 23:27 4
Can a model be changed to have a finite expectation?
Still, we do not want the extreme upper tail to have much influence. If $X$has a finite expectation, then we can change the model to have a hard upper limit without undue influence to the model. In situations with a fuzzy upper limit that seems good.