# Tagged Questions

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### Distribution of Product of Normal and Poisson?

Suppose that X is distributed Poisson with a known rate and Y is a normal distributed with a know mean and variance. My goal is to approximate the distribution Z where P(Z) = P(X) * P(Y), where Z is ...
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### Accessible, free introduction to Stein's method?

Does anyone know of video lectures, tutorials, and/or books that are free and serve as an accessible introduction to Stein's method? Background: I have taken the first year PhD probability course ...
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### Does the normal approximation get better as a density becomes more peaked?

I have a sequence of densities $f_n(x_n)$, of random variables $X_n$, with means $\mu = 0$ and variances decreasing with $n$: $$\sigma^{2}(X_n) = \frac{\sigma^2}{n}.$$ I am approximating $f_n(X)$ ...
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### Minimum enclosing Gaussian

Given two weighted Gaussians with arbitrary weight, mean and variance, what is the parameters of the minimum enclosing Gaussian? The mean and variance should be chosen such that the weight is minimum ...
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### Using continuity correction for normal approximation or not?

Below is a question on a recent actuarial exam, Exam 3L of the CAS. I didn't know whether or not to use the continuity correction when using the normal approximation to do hypothesis testing ...
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### Approximate distribution of normal squared

I am studying for a test, one section of which will cover the delta method. This problem came from that section: Let $X\sim N(\mu,n^{-1})$. Find an approximate distribution of $X^2$. (It also asks ...
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### Normal approximation to the binomial distribution

I am having trouble getting to the bottom of this concept for two types of questions (hw is already passed, but I have a test this week and would like to do better). Hopefully someone can help me get ...
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### What is the normal approximation of the multinomial distribution?

If there are multiple possible approximations, I'm looking for the most basic one.
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### Error in normal approximation to a uniform sum distribution

One naive method for approximating a normal distribution is to add together perhaps $100$ IID random variables uniformly distributed on $[0,1]$, then recenter and rescale, relying on the Central Limit ...
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### How to compute the probability associated with absurdly large Z-scores?

Software packages for network motif detection can return enormously high Z-scores (the highest I've seen is 600,000+, but Z-scores of more than 100 are quite common). I plan to show that these ...
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### Approximate order statistics for normal random variables

Are there well known formulas for the order statistics of certain random distributions? Particularly the first and last order statistics of a normal random variable, but a more general answer would ...
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### Evaluate definite interval of normal distribution

I know that an easy to handle formula for the CDF of a normal distribution is somewhat missing, due to the complicated error function in it. However, I wonder if there is a a nice formula for ...
Assume I have a random vector $X = \{x_1, x_2, ..., x_N\}$, composed of i.i.d. binomially distributed values. If it would simplify the problem substantially, we can approximate them as normally ...