12 questions linked to/from Test for finite variance?
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### How to tell if a sample comes from a distribution with infinite mean? [duplicate]

I observe a sample from a distribution that I expect to be the hitting time $$\tau = \inf\{t>0| X(t)>a\}$$ where $X(t)$ is a Lévy process with $X(0)=0$ and $a$ is some constant. $X$ is not a ...
1 vote
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### How do we determine if the true population distribution has a finite mean and/or variance? [duplicate]

Some distributions do not have finite/defined mean/variance: How can a distribution have infinite mean and variance? Is there a way to determine from your sample if the population distribution has ...
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### Is normality testing 'essentially useless'?

A former colleague once argued to me as follows: We usually apply normality tests to the results of processes that, under the null, generate random variables that are only asymptotically or ...
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### What is the difference between finite and infinite variance

What is the difference between finite and infinite variance ? My stats knowledge is rather basic; Wikipedia / Google wasn't much help here.
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### When to use Student's or Normal distribution in linear regression?

I am looking at some problems, and in some, to test the coefficients, sometimes I see people using Student's distribution, and sometimes I see Normal distribution. What is the rule?
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1 vote
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### Need an example of RV with a mean and no second moment

An example like the t-distribution with 2 degrees of freedom would not suffice as the second moment exists but equals inf.
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### When is uniform distribution have maximum entropy instead of normal distribution?

As far as I know, when we have just data and no constraints (other than probabilities must add up to 1), the distribution that gives maximum entropy is uniform distribution. But when we know mean and ...
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### Hypothesis testing involving pathological distributions

Given a very large number of samples $n$ from the population, suppose that I am trying a standard hypothesis test on the means: \begin{align}H_0:&\overline{x}\leq\mu_0\\ H_1:&\overline{x}&...
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### How to check if a distribution has undefined variance?

How can I determine if experimental data comes from a distribution where the variance is undefined (e.g. the Cauchy distribution)? I honestly have no idea how to attack this problem in a sensible way,...
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