# Tagged Questions

Moments are summaries of random variables' characteristics (e.g., location, scale).

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### Unbiased estimator variance of sample variance

I was reading the section on k-statistics on wolfram alpha. It was known to me that for the sample variance $k_2 = \frac{1}{n-1}\sum_{i=1}^n (x_i - \overline{x})^2$ it holds that its variance ...
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### Linear moment inequality for layman

Can someone please explain Manski approach to partial identification in very basic terms? I have gone through a lot of stuff but failed to find an intuitive explanation. I also don't understand how ...
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### Does a scaling and shift of first two moments change higher moments too?

For a given random variable $X$ with mean $\mu_{\mathrm{old}}$ and standard deviation $\sigma_{\mathrm{old}}$ I would like to perform a transformation $g$ to obtain a new random variable $Y := g(X)$ ...
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### If you know the central moments of the data $X$, find a function $f$ for which $f(X)$ has arbitrary central moments

Say you are given one-dimensional data $X$, with mean $\mu$ and central moments $a_n$ which you know. Can you construct a function $f(x)$ which transforms the data such that $f(X)$ has the central ...
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### Why is a moment called a moment? [duplicate]

Someone told me that the term "moment" in Statistics comes from Physics. But I fail to understand how it relates to the definition of a moment of a force, which is a measure of its tendency to cause a ...
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### Normalizing skewness with the Power or Box-Cox Transformation

Suppose I have a random sample drawn from an arbitrary strictly positive continuous distribution. Suppose moreover that I want to use the Box-Cox transform to zero out the skewness. Is there an ...
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### How to combine statistical moments at different orders?

I am performing a number of simulations involving the estimation of statistical moments at different orders (lets say, from the 1st till the 3rd order). For certain case studies, I have useful ...
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### Derivation of the third moment of the count joint statistic

Does anyone know where I can find the derivation of the third moment of the joint count statistic? I found this similar question answered in the past: need derivation of join-count variance (spatial ...
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### Rule of thumb for number of observations required to estimate moments

I have a vague memory of reading about a rule of thumb for how many observations are required to estimate each moment. i.e. that to estimate the mean you need at least x observations, to estimate the ...
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### Covariance for three variables

I am trying to understand how covariance matrix works. So let's suppose we have two variables: $X, Y$, where $\text{Cov}(X,Y) = \mathbb{E}[(x -\mathbb{E}[X])(y-\mathbb{E}[Y])]$ gives the relation ...
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### How can I scale the $k$-th moment of a time series to a different time frequency?

I have a time series, let's say N daily log-returns. I want to study the moments (possibly the distribution) of the weekly returns. I have two ways: 1) Using the time-additivity property of ...
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### Are moments related to moments in physics? [duplicate]

The terms are the same, but I cannot outwardly see, whether moments in statistics have something to do with moments in physics. So are they related? How?
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Simple question, yet surprisingly difficult to find an answer online. I know that for a RV $X$, we define the kth moment as $$\int X^k \ d P = \int x^k f(x) \ dx$$ where the equality follows if $p = ... 0answers 92 views ### Higher-order cumulant and moment names beyond variance, skewness and kurtosis In physics or mathematical mechanics, starting from position$x(t)$, one obtains rates of change via derivatives with respect to time: velocity, acceleration, jerk, jounce (4th order). Some have ... 0answers 20 views ### What does the MGF do when its parameter is other than 0? I've only seen the MGF used when it takes 0 as it parameter and then derived for the nth moment. What does the MGF tell us when the parameter is other than 0? 1answer 79 views ### What is “t” in generating functions? I am studying generating functions applied to probability (moment generating functions, probability generating functions and characteristic functions). I perfectly see their purposes and usefulnesses, ... 1answer 54 views ### Convergence of expectation Suppose we have$X_n \overset{D}\to X$for some sequence$X_{1},\dotsc, X_{n}$. Is it the case that if$E(X_{n}^2) \to E(X^2)$we have it that$E(X_n) \to E(X)$, and when would it hold? My first ... 1answer 61 views ### What is the effect of taking the mean of a moments-based estimate? Suppose I estimate the second and fourth moments of a signal as$M_2 \approx \frac{1}{N} \sum_{n=0}^{N-1} | y_n |^2$and$M_4 \approx \frac{1}{N} \sum_{n=0}^{N-1} | y_n |^4$and then I use these ... 1answer 34 views ### Approximate estimation of a covariance involving ratios I have three random variables (T, O, A) that are each approximately normal. These three random variables are combined to form two ratios: X=T/A and Y=O/A. I wish to get an estimate of the covariance ... 0answers 11 views ### Empirical validation of a regression model estimating the mean and the variance? I would like to empirically validate over a given dataset a regression model$\mathbb{R}^n \to \mathbb{R}^2$that outputs both the mean and the variance. In particular, I am seeking a metric that ... 1answer 47 views ### First and second moments of deep nesting of the Binomial-Binomial hierarchical model? I am interested in the Binomial-Binomial hierarchical model, where the number of trials itself follows a binomial distribution. I would like to know the expected value (first central moment,$\mu_1\$) ...
Suppose that I have n observations, $$X_1,...,X_n$$ with unknown distribution, n being small (say, between 6 and 20). If I know the first four sample moments (average, standard deviation, skewness, ...