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# Questions tagged [moments]

Moments are summaries of random variables' characteristics (e.g., location, scale). Use also for fractional moments.

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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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### Simulate a distribution from a fitted beta-regression model for a density plot in R [duplicate]

I have produced the following figure by simulating some values from a fitted gamma regression with a low AIC value that provides the closest approximation of my raw data out of all of my models, and ...
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### Central limit theorem : relaxing assumption of all finite moments

Consider $S_n = \sum_{i = 1}^n b_{i,n} X_{i,n}$ where $X_{i,n}$ are random variable neither independent neither identically distribution and $b_{i,n}$ are weights satisfying the Lindeberg condition. I ...
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