Extreme values are the largest or the smallest observations in a sample; e.g., the sample minimum (the first order statistic) and the sample maximum (the n-th order statistic). Associated with extreme values are asymptotic *extreme value distributions.*
2
votes
1answer
90 views
Asymptotic probability concerning the largest absolute value in an iid Gaussian sample
Let $v[n]$ be a vector $N$ $iid$ gaussian samples, of ~$N(0,\sigma^2)$ Also, let $v_{max}$ denote the maximum absolute value of all the samples given. (That is, if I took the absolute value of all the ...
1
vote
1answer
60 views
What do I need to consider when using the Hessian to computer S.E.'s?
I use optim() in R to do a lot of MLE. I've used the approach for a lot of problems, but the one I'm working on right now consists of fitting the parameters of the generalized extreme value ...
0
votes
1answer
58 views
Fitting GEV to non-stationary time series of extremes (general stationarity question?)
I'm fitting the generalized extreme value distribution (GEV) to a series of annual maxima of variable $X$. $X$ exhibits a linear trend.
When I fit the GEV to $X$, I think I have the choice to
Use ...
1
vote
1answer
56 views
Expected value of latent utility in logistic regression
I'm looking for an analytical expression for the expected value of the latent utility in a logistic regression.
Setup:
There are two choices indexed by $i \in \{0, 1\}$ with associated utilities ...
1
vote
1answer
19 views
How to test the significance of increase in sample interval range(s)?
Suppose we have two samples of a variable taken under different conditions: e.g. A1 without medical treatment and A2 after medical treatment. These are not necessarily normally distributed. Suppose A1 ...
0
votes
0answers
75 views
Value at risk by Monte Carlo using generalized Pareto distribution
I have created a VBA program to calculate VaR by using Monte Carlo, I have simulated Brownian Motion. This method might be ok for 100% equity portfolio, but let's say this portfolio may have fixed ...
1
vote
0answers
70 views
Confidence intervals for extreme value distributions
I have wind data that i'm using to perform extreme value analysis (calculate return levels). I'm using R with packages 'evd', 'extRemes' and 'ismev'.
I'm fitting GEV, Gumbel and Weibull ...
1
vote
0answers
26 views
Non-Analytic extrapolation
I have some samples of a stable real-world process. Its is polymodal, and does not cleanly fit any of the "textbook" analytic distributions. I need to make very accurate estimates of the maximum ...
1
vote
0answers
69 views
Probability of exceedance and reliability of a sample range estimation
Consider that $P$ is the water pressure coming out of a valve $A$. Let $P_{dif}$ be the difference between the maximum and the minimum pressure of valve $A$:
$$P_{dif}≔P_{max}-P_{min}$$
Now, what I ...
1
vote
2answers
409 views
Determine density of min(x,y) and max(x,y) for independently uniform distributed variables
Two independent random variables, X and Y, are uniformly distributed on the unit interval (-1,1).
Determine the density for U=min(X,Y) and for W=max(X,Y)
1
vote
0answers
162 views
Calculation of confidence interval of a population parameter
Consider that $P$ is the water pressure coming out from a valve A. Let $P_{dif}$ be defined as the difference between the maximum and the minimum pressure of valve A:
$$P_{dif}:= P_{max} - P_{min}$$
...
1
vote
1answer
32 views
Learning to predict maximum of parameterized function class
I am interested in a multi-task regression problem: I have a parametrized function $f_x : \mathcal{R}^n -> \mathcal{R}$ where $x \in \mathcal{R}$ is a real-valued parameter. For some values of $x$, ...
3
votes
0answers
36 views
fitting the tail of a distribution in a regression tree
I have 3 integer valued time series $a_t$, $b_t$ and $y_t$ with $k$ observations. I want to fit $y_t$ with the 2 first, and for that purpose I use a regression tree like this:
test all combinations ...
1
vote
1answer
90 views
How to assess the quality of a return period estimate?
Background
I have a time series of structural loads, which are measured forces on a moored ocean buoy, and I need to obtain the return period value so that the structure can be designed to withstand ...
2
votes
0answers
106 views
Random Forest Regression - Coping with extreme values
I'm not sure if I used the concept "extreme values" right. Anyhow, I'm trying to produce a model that estimates maximum tree heights / km^2. I have a database of around 24000 points (km^2), each has ...
21
votes
7answers
889 views
Taleb and the Black Swan
Taleb's book "The Black Swan" was a New York Times best seller when it came out several years ago. The book is now in its second edition. After meeting with statisticians at a JSM (an annual ...
4
votes
1answer
94 views
What is the maximum value in a finite selection of a normally distributed variable?
A parameter of an object is normally distributed with a mean m and a std. dev. s. If r such ...
5
votes
2answers
319 views
Asymptotic distribution of maximum order statistic of IID random normals
Is there a nice limiting distribution of $\max( X_1,X_2,...,X_n) $ as $n$ goes to $\infty$, assuming that they are iid normal distributions with variance $\sigma^2$.
This is almost certainly a well ...
1
vote
1answer
59 views
Meaning of return period on extreme events
If the distribution of the periods between an extreme event to another is a power law (as for example can be the return period of extreme earthquakes or flooding), the existence of the mean value is ...
1
vote
0answers
110 views
How to calculate the boundary value for a random variable which is sum of variables with gamma and uniform distributions?
The variable is a sum of two random variable which obey gamma and uniform distributions, respectively. The parameters of the uniform distribution variable are determined, and the other's must be ...
2
votes
1answer
146 views
Uniform distribution & generation of extreme values in R
I'd like to generate a new point which should be uniformly distributed on the interval [a, b) (i.e. including the left extreme value - a and exluding the right extreme value - b). The ...
0
votes
0answers
157 views
Algorithm for finding all local maxima of a boosted regression tree?
Given a weighted sum of regression trees, is there an efficient algorithm to find all local maxima ?
(I would tend to think that a gradient based method will find some maxima but it is not entirely ...
2
votes
2answers
146 views
Predicting a maximum value with little data
My problem is i'm trying to figure out how many servers might be required to handle a theoretical maximal load of data requests. To do that I need to know what the maximum number of requests in a ...
4
votes
1answer
368 views
How to apply Mahalanobis weighted regression in R?
Some research has shown that in linear regression applications the Mahalanobis distance approach can be used to perform regressions that lower the influence of outliers. The idea is that in the ...
1
vote
1answer
132 views
The min draw from F(x), where the max is an order statistic of the max draws from different, yet overlapping distributions?
Consider $m$ independent draws from each of $n$ distributions. $X_{i,j}$ the $i_{th}$ draw from cdf $F_{j}(x)$. where $1 \leq i \leq m$ and $1 \leq j \leq n$. Therefore we have $m\cdot n$ total ...
7
votes
2answers
482 views
What is the distribution of maximum of a pair of iid draws, where the minimum is an order statistic of other minima?
Consider $n\cdot m$ independent draws from cdf $F(x)$, which is defined over 0-1, where $n$ and $m$ are integers. Arbitrarily group the draws into $n$ groups with m values in each group. Look at the ...
-1
votes
1answer
333 views
How to get expectation (E-value) for a dataset?
I wonder if experts could teach me how to solve this questions.
For an examination, scores for 10 students (all from class 4B) were obtained. I want to convert each score to E-value.
If I ...
2
votes
2answers
475 views
Is my data fit “extreme value distribution” or “normal distribution”?
I have a large data.frame in R. I would like to double if its distribution fit normal distribution or extreme value distribution better
Here is my simplified data.frame.
...
3
votes
2answers
263 views
Calculating the distribution of maximal value of $n$ draws from a normal distribution
According to normal probability distribution theory which says that for $n$ independent,
identically distributed, standard, normal, random variables $\xi_j$ the expected absolute maximum is
...
6
votes
1answer
163 views
Estimate the nearest of N random points in a box in E^d?
I have N uniform-random points $p_j$ in a box in $E^d$,
$a_i \le x_i \le b_i$,
and want to estimate the expected distance of the point nearest the origin in $L_q$:
$\quad$ nearest( points $p_j$, box ...
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 ...
4
votes
1answer
96 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 ...
2
votes
1answer
122 views
Basics of extreme values / high-water marks?
With real-valued $X_1, X_2, \ldots$, define
$Max_n := \max(X_1,\ldots,X_n)$ record value or high-water mark
$NextMax_n :=$ the next greater high water, $Max_{n+m} > Max_n$
$Up_n := NextMax_n - ...
