All Questions
Tagged with extreme-value estimation
16 questions
3
votes
3
answers
125
views
What statistic best estimates the sample mean in case of missing data in a distribution?
I have samples of particles and am interested in the particle lengths. The problem is that the samples are assessed using image analysis. As the particles overlap, the measurements are incomplete and ...
- 165
7
votes
1
answer
411
views
Estimation of a uniform distribution corrupted by Gaussian noise
Problem definition
I have a dataset composed by $m$ observations $y^{(1)},\dots,y^{(m)} \in \mathbb{R}^2$ generated as follow
\begin{equation*}\begin{aligned}
y &= z + v \newline
z & \sim\...
- 473
0
votes
0
answers
42
views
Is modeling the extreme value of a distribution a basic probability result?
I was reading briefly about the field of EVT - extreme value theory, and the associated distributions that arise from modeling the maximum of a finite sample. It's not quite clear to me the nature of ...
- 64.8k
2
votes
0
answers
133
views
Is there any intuitive explanation for MoM in estimating parameters?
I found from some literature that when we use the method of moments to fit the Gumbel distribution, the estimated
(On page 24) A comparison of the variance formulas in (1.66) with the CramBr-Rao ...
- 747
4
votes
0
answers
75
views
Estimation of the density at the bound of the support of a real random variable
Let $X$ be a random variable with real values and with density $f$.
Assume the support $f$ is bounded with supremum $m$ and has a positive value at that supremum:
$$\forall x > m, f(x) = 0 \text{ ...
- 2,629
2
votes
0
answers
49
views
MLE for the number of samples given $k$ largest values
I have the views on the top 100 videos using a tag in TikTok and want to estimate the total number of videos in that tag. I know the distribution for other tags so I can make a guess as to what it is ...
- 2,608
2
votes
2
answers
1k
views
Estimating the min and max of a distribution
I have a measurement problem where I am attempting to measure the minimum and maximum height of a surface by taking point samples of heights. If I then look at the distribution of all height values, ...
- 177
1
vote
3
answers
3k
views
Estimating max value from statistical data
Assuming that you have the following values for a data set:
Median
Mean
First quartile
Third quartile
Standard deviation
Number of elements
Minimum value
, would it be possible to somewhat ...
- 11
3
votes
1
answer
215
views
Finding mode using mean and skewness (and higher moments)?
I have a pdf that doesn't yield trivial derivatives, so I cannot differentiate it and find the root to determine where its max exactly occurs.
However, I have a general formula to express all its ...
- 33
1
vote
0
answers
88
views
Maximise the probability of a linear combination of random variables
I have a data set representing a random vector $\mathbf{X}=(X_1,\ldots, X_p)'$.
Define $Z=\alpha' X $, where $\alpha \in \mathbb{R}^p$ and $\alpha'\mathbf{1}_p =1$.
I would like to find the $\alpha$ ...
- 163
2
votes
1
answer
455
views
Likelihood for dependent data above a threshold
Let $(Y_t)$ a real-valued stationary Markov chain and $u$ some positive threshold. We assume that for $y>u$,
$$Y_{t+1}|\{Y_t=y\}\sim\mathcal{N}(\alpha y+\mu y^\beta,\sigma^2 y^{2\beta})$$
I want ...
- 233
4
votes
2
answers
955
views
R - MLE of modified Champernowne density
I've come across an article (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=704903), in which author wrote about maximum likelihood estimates of parameters in the so called modified Champernowne ...
- 349
2
votes
1
answer
51
views
Estimating costs with extreme values
I am trying to estimate health care costs and I was wondering what the standard practice is for extreme values?
By extreme values I mean I have a large portion of my costs being zero and a small ...
- 979
7
votes
1
answer
298
views
Name for the special estimate of the mean
During my masters studies, I heard about the following estimate of the mean: We take the minimal and the maximal value from sample and simply average them out.
Does this estimate have any name? And ...
- 3,979
5
votes
2
answers
2k
views
Expected maximum given population size, mean, and variance
How would one estimate the maximum given population size, a few moments, and perhaps some additional assumption on the distribution?
Something like "I'm going to do $N_s≫1$ measurements out of ...
- 205
6
votes
1
answer
483
views
Quantile extrapolation?
Suppose you wanted to estimate the $q$ quantile of a distribution by observing $n$ independent draws from that distribution, but with $q < \frac{1}{n}$. What methods are available, and for what ...
- 15k