Questions tagged [moments]
Moments are summaries of random variables' characteristics (e.g., location, scale). Use also for fractional moments.
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Delta Method and the Variance Convergence
In the references I've seen, the $\Delta$-method is typically formulated in terms of convergence in distribution: for $X_i$ i.i.d., $\mathbb{E}[X_i]=\mu$ and $\mathrm{Var}_\mu(X_i)=\sigma^2<\infty$ ...
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Isn't kurtosis poorly defined if it doesn't take into account skewness?
Apologies in advance, I am not a statistician so this question may be naive. The way I understand things is as follows:
The mean is the first raw moment.
Variance is the second central moment, i.e. ...
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Proving that mgf determines distribution via Laplace transform
I am reading this question and the answer provided there about the moment generating function (mgf) and how its uniqueness can be proved via the uniqueness of Laplace transforms. In my book, Measure ...
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Second moment of weighted average of random variables
I stumbled upon problem 254 from the SOA Exam P list in
https://www.soa.org/globalassets/assets/Files/Edu/edu-exam-p-sample-quest.pdf
for which I am puzzled by the solution described in
https://www....
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Relation between first three moments of distribution
Consider a random variable $X$ with distribution described by the first three moments:
$$\mathbb{E}(X) = \mu$$
$$\mathbb{E}(X-\mu)^2 = \sigma^2$$
$$\mathbb{E}(X-\mu)^3 = \gamma$$
Is there a nontrivial ...
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Estimating correlation parameter from known value of bivariate normal distribution
I want to estimate the correlation parameter $\rho$ using the following expression taken from this paper (equation 10 on page 17):
$$ \hat{s}^2+\hat{\mu}^2=N_2(N^{-1}(\hat{\mu}),N^{-1}(\hat{\mu}), \...
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Higher order moments to evaluate strength of linear relationship between variables
Let $X_1,\dots,X_n$ be real random variables such that $\alpha_1X_1+\dots+\alpha_nX_n=0$ for some unknown $\alpha_1,\dots,\alpha_n$. If $n=2$, one can study the strength of linear relationship by ...
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By means of what distribution can I match the first n moments for arbitrary (i e. any) values of those moments?
Suppose I have the first n moments from some data set, either raw, centered or scaled, (or cumulants instead) whichever is more convenient for matching. Is there a continuous, continuously ...
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How can I implement moment matching with kernel tricks if I do not have the complete distribution but only the higher-order moments or culuments?
As is said in Appendix B.3 of ref, "It is difficult to match high-order moments, because we have to deal with high order tensors directly. On the other hand, MMD can easily match high-order ...
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Moment Ratios and L Moment Ratios:
I want to know the difference between moment ratio diagrams and L moment ratio diagrams.
As I understand the moment ratio diagram serve the purpose of detecting the type of probability density ...
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Terminology clarification about sample moments
According to MathWorld (link): "The sample raw moments are unbiased estimators of the population raw moments".
While in Wikipedia (link) it is said:
...the $k$-th raw moment of a population ...
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$\mathbb{E}[X^2]\leq k \mathbb{E}[X]^2$, upper bound second moment from first moment
Let $X$ be a non-negative random variable bounded on $[0,1]$. Is it true that $\mathbb{E}[X^2]\leq k \mathbb{E}[X]^2$ for some constant $k$? If not, are there any minimal assumptions on $X$ where this ...
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Why do the skewness and kurtosis formulae have powers of the variance in the denominator?
We calculate the variance as the centered 2nd moment $E[(X-\mu)^2]$.
So when it comes to the skewness and kurtosis, why are the 3rd and 4th moments divided by the 3rd and 4th powers of $\sigma$? Why ...
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what is the formula for calculation of fourth raw moment (or central moment) from variance and 3rd central moment (or raw moment)?
Basically the title. I can't seem to find any solution for this.
I have the mean, variance or the second central moment and third central moment and third raw moment. I need to find the fourth raw ...
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Characterize conditions in which Taylor moment approximation is good
I am working with the Projected Gaussian, or Angular Gaussian distribution, which is given by $z = \frac{x}{||x||}$, where $x \sim \mathcal{N}(\mu, \Sigma)$. This is a distribution on the sphere in $\...
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