Linked Questions

5 votes
0 answers

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 ...
user29514's user avatar
1 vote
0 answers

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 ...
confused's user avatar
  • 3,063
372 votes
15 answers

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 ...
shabbychef's user avatar
  • 14.3k
46 votes
4 answers

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.
AfterWorkGuinness's user avatar
10 votes
2 answers

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?
Leo's user avatar
  • 101
1 vote
2 answers

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.
Seeking Knowledge's user avatar
2 votes
1 answer

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 ...
ikadorus's user avatar
3 votes
0 answers

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}&...
M.B.M.'s user avatar
  • 1,069
5 votes
1 answer

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,...
Hooked's user avatar
  • 441
4 votes
0 answers

Test for Lipschitz continuity (is there some?)

Let $x_1, \dots, x_n$ be a random sample from a distribution $D$. Say, I want to test whether $F(z)$, the cdf of $D$, is Lipschitz continuous, i.e. there exists $L$ such that $F(z + \delta) - F(z) \...
Tomas's user avatar
  • 415
6 votes
1 answer

Is it possible to construct a hypothesis test for the existence of a mean of a symmetric distribution?

In practice, we often assume that the process we are examining has a mean, and so statistics involving averages are defined. As pure conjecture, I was wondering if one can construct a hypothesis test ...
user avatar
3 votes
0 answers

Are there correct papers describing tests for finiteness of ($k$th) moments?

Note: A previous question asking about the finiteness of second moments was asked in 2010 -- this question is not a duplicate of that one because (1) this question is about tests for the finiteness of ...
Chill2Macht's user avatar
  • 6,109