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Results tagged with moments
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user 247274
Moments are summaries of random variables' characteristics (e.g., location, scale). Use also for fractional moments.
2
votes
1
answer
2k
views
Estimation of the second moment and square root of the second moment (not variance and stand...
I want to estimate the second moment of a distribution. I know the breakdown of the second moment into the mean-squared and variance: $\mathbb{E}[X^2] = (\mathbb{E}[X])^2 + var(X)$.
When I want to est …
- 67.1k
8
votes
0
answers
439
views
What does the second moment tell us that variance does not?
What does the second moment tell us that variance does not?
I can wrap my brain around what the first moment tells us, and I can wrap my brain around what the variance tells us, but interpreting the …
- 67.1k
11
votes
2
answers
861
views
Westfall says, "the proportion of the kurtosis that is determined by the central $\mu\pm\sig...
In his article that debunks the notion of kurtosis as measuring distribution peakedness, Peter Westfall writes,
[T]he proportion of the kurtosis that is determined by the central $\mu\pm\sigma$ range …
- 67.1k
0
votes
0
answers
83
views
Decomposition of the second moment of a circular distribution
When we have a "usual" random variable $X$ on the real line, we can break down the second moment.
$$
\mathbb{E}[X^2] = (\mathbb{E}[X])^2 + var(X)
$$
Is there an equivalent for a circular distribution …
- 67.1k
1
vote
0
answers
95
views
When would correlation between two variables not exist?
If we have two random variables $X$ and $Y$, then $\text{corr}(X,Y)=\dfrac{
\text{cov}(X,Y)
}{
\sqrt{
\text{var}(X)\text{var}(Y)
}
}$.
This correlation will not be defined if either variable has an un …
- 67.1k
11
votes
2
answers
729
views
Independence of Mean and Variance of Discrete Uniform Distributions
In the comments below a post of mine, Glen_b and I were discussing how discrete distributions necessarily have dependent mean and variance.
For a normal distribution it makes sense. If I tell you $\b …
- 67.1k