Tagged Questions
0
votes
0answers
49 views
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 ...
1
vote
1answer
51 views
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 ...
1
vote
1answer
55 views
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 ...
2
votes
3answers
466 views
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 ...
2
votes
1answer
653 views
What is the normal approximation of the multinomial distribution?
If there are multiple possible approximations, I'm looking for the most basic one.
9
votes
1answer
473 views
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 ...
9
votes
3answers
922 views
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 ...
10
votes
3answers
2k views
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 ...
10
votes
3answers
935 views
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 ...
5
votes
3answers
417 views
How do extreme values scale with sample size?
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 ...
2
votes
1answer
248 views
Central Limit Theorem Tails
I'm trying to compute some p-values for samples from a distribution of sums of ~1000 random variables. The exact distribution of these random variables isn't known, but I have empirical estimates that ...
