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What is finite mean and variance?
1. Important point: if variance of a population is infinite, but variance of a sample is finite, then any estimate of the population’s variance or standard deviation using a sample statistic like s2, or s, then s√n will be rather badly biased.
Does finite variance implies finite mean?
Assume that a random variable has a finite variance. Does it mean it also has a finite mean? My approach: I think since it has a finite variance, it means it is in L2 space of the probability measure μ. Therefore, it should be in L1 space of the probability measure μ and thus the mean is finite.
Can you have an infinite variance?
Models with infinite variance have right tails that extend to infinity. Distributions with infinite variance have fat upper tails that decrease at an extremely slow rate.
How do you know if variance is finite?
If the smaller tail index is greater than 2, then the random variable has a finite variance, when it is between 1 and 2, the random variable has a finite mean but an infinite variance, and when it is less than 1, the random variable does not have a finite mean.
Do financial returns have finite or infinite variance?
(1990) report statistical evidence of finite variance in financial returns. In particular, one could find, for example, that daily or more frequent returns had infinite variance, but weekly or less frequent returns had finite variance.
What is a finite standard deviation?
If the population standard deviation is finite, the standard error of the mean of the sample will tend to zero with increasing sample size, because the estimate of the population mean will improve, while the standard deviation of the sample will tend to approximate the population standard deviation as the sample size …
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
What’s the difference between infinite and finite expectation?
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. If the model have infinite expectation, then, any hard upper limit we introduce to the model will have dramatic consequences!
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.