All Questions
Tagged with sum central-limit-theorem
8
questions
2
votes
0
answers
81
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When is $\sum Z_i \sim \sqrt{n} Z_i$?
If $X_i$ are independently and identically distributed $N(0,\sigma^2)$ then $Y=\sum X_i \sim N(0,n\sigma^2)$, i.e. $\sum X_i \sim \sqrt{n}X_i$. That raises two questions:
Is a zero-mean normal ...
- 40.5k
0
votes
1
answer
114
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How to apply Lyapunov CLT to data
I have a situation where I have around 30 classes of variables with different means and variances (though the means aren't too far from eachother; think 4-7) and that the distributions are right ...
- 145
2
votes
1
answer
34
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Limiting distribution of infinite sparse sum
Let $N$ be a positive integer.
I consider $N$ random variables $X_1^{(N)}, X_2^{(N)}, \dots, X_N^{(N)}$, all independent and identically distributed, each taking values $\pm 1$ with probabilities $p/(...
- 4,440
4
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Does the sum of discrete uniforms converge to a discrete Gaussian?
Is there some analogous of the Central limit theorem for discrete uniforms and discrete normal distributions?
To be more specific, let's say we have identical and independent random random variables $...
7
votes
0
answers
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Square roots of sums absolute values of i.i.d. random variables with zero mean
In an earlier question, I asked about the limiting distribution of the square root of the absolute value of the sum of $n$ i.i.d. random variables each with finite non-zero mean $\mu$ and variance $\...
- 40.5k
2
votes
1
answer
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Sum of random variables without normalization approaches gaussian
The central limit theorem states that the limiting distribution of a centered and normalized sum of independent random variables with mean $\mu$ and finite variance $\sigma^2$ is Gaussian.
$$
\frac{\...
- 125
13
votes
1
answer
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Central Limit Theorem for square roots of sums of i.i.d. random variables
Intrigued by a question at math.stackexchange, and investigating it empirically, I am wondering about the following statement on the square-root of sums of i.i.d. random variables.
Suppose $X_1, X_2, ...
- 40.5k
5
votes
2
answers
448
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Sum of random variables without central limit theorem
I know that using central limit theorem we approximate sum of random variables into Gaussian distribution. Is the any other approximation method available for finding the probability distribution ...
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