All Questions
5 questions
3
votes
2
answers
1k
views
Expected value of a truncated binomial
Let $X\sim B(n,p)$ be a binomial random variable and fix $0<k<n$. Are there any well-known bounds for $\mathbb{E} (X-k)^+$, where $(X-k)^+ =\max\{0,X-k\}$? I am particularly interested in ...
- 4,049
1
vote
1
answer
144
views
A uniform mixture of order statistics
Let $0<k<n$ be integers, and let $X$ be a random variable obtained as follows: sample $n$ points independently and uniformly at random in the unit interval, and select (uniformly) one of the $k$...
- 4,049
1
vote
0
answers
103
views
Convergence result on Cornish Fisher expansion of binomial distribution
Since it is known that Cornish Fisher expansion of quantiles does not have guaranteed convergence for all distribution, I wonder specifically if any convergence result is known in literature for CF ...
- 53
11
votes
1
answer
1k
views
What are some of the surprising results of finite sample statistical estimation?
I'm trying to familiarize myself with the latest results in finite sample statistics. It seems to me that these results can be classified into two categories:
Unsurprising results confirm that the ...
- 395
2
votes
1
answer
295
views
The asymptotics of $\int_{-\infty}^{\infty} \phi(x) {\Phi(\frac{x}{a})}^{qa} dx $ for normal distribution using saddle point approximation
In my probability and numerical analysis research I have come across the following predicament:
If we have a standard normal random variable X with CDF $ \Phi $, and PDF $ \phi $ I am interested in ...
- 620