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4 votes

How to show that many functions (a hundred, a thousand) have the same shape an distribution of values over an interval?

To show that several functions are more or less the same you could just superimpose them graphically. I don't think quantile plots of any flavour are directly relevant or likely to be helpful. The ...
Nick Cox's user avatar
  • 58.6k
2 votes

Is considering a specific distribution necessary before computing an average?

The other answers are correct about the validity of computing the mean. However when you "use those computed averages to represent measures of variables", there is a caveat. Let's say the ...
Alexlok's user avatar
  • 165
2 votes

Is considering a specific distribution necessary before computing an average?

The mean (average) is a descriptive statistic, just like the variance (standard deviation), skewness, or the coefficients of a linear regression, etc. They are just the mathematical results of ...
jginestet's user avatar
  • 1,969
2 votes

Is considering a specific distribution necessary before computing an average?

You do not need to know the distribution of the average to use it. Suppose the observations are assumed to be independent and identically distributed. In that case, the estimated expected value of the ...
Xiaochuan Lu's user avatar
1 vote

Location shift of two distributions

Yes, the conditional higher-order central moments are all the same Since $X$ and $Y$ are independent, the conditional expectation has the following form: $$\begin{align} \mu(y) &\equiv \mathbb{E}[...
Ben's user avatar
  • 129k
1 vote

How can I find the limiting distribution of $Z_n=\sqrt{n}\frac{X_1X_2+X_3X_4+\cdots+X_{2n-1}X_{2n}}{X_1^2+\cdots+X_{2n}^2}$?

Let $X_1, X_2, \cdots$ be i.i.d. random variables with $E(X_i) = 0$, $\text{Var}(X_i) = 1$, and $E(X_i^4) < \infty$. We are tasked with finding the limiting distribution of $$ Z_n = \sqrt{n} \frac{...
Robert Long's user avatar
  • 64.1k

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