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.*

learn more… | top users | synonyms

0
votes
0answers
16 views

Extreme value simulation @ Monte Carlo

Folks, I would like to seek your help with some questions to simulating extreme values. For example, I have written the following R code to generate QQplots for a normally distributed data, varying ...
0
votes
0answers
5 views

Best method to fit a GEV distribution with generalised linear modelling of parameters?

I need to fit a generalised extreme value distribution to my data but I want the ability to perform generalised linear modelling of the parameters, particularly the location. Can anyone recommend the ...
0
votes
0answers
15 views

Smallest Spectral Norm / Deviation Inequality

Consider $A_{m \times n}$ be an i.i.d. random matrix with finite first to fourth moments. There is a good number of asymptotic and non-asymptotic results regarding the spectral norm of $A$, $\|A\|_2$, ...
1
vote
0answers
16 views

Extreme value distribution for multivariate normal

I have a series of data sets. Each data set represents a measurement in 3D space relative to a global origin. I want to model the extreme values of my data. If I were to calculate the extreme radius ...
0
votes
1answer
28 views

Lévy stable vs. extreme value distributions

I'm trying to understand the advantages (if any) of employing the Generalized Extreme Value distribution (GEV) vs. a stable distribution in the context of understanding the probability of crossing a ...
1
vote
0answers
28 views

Repairable system and the sum of GEV random variables

We know that $X\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ and $Y\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ then $X+Y\sim {\mathrm {Logistic}}(2\alpha ,\beta )$. I am wondering, what will be $X+Y+Z$ ...
1
vote
0answers
44 views

Conceptual or mathematical motivation for the three extreme value distribution types?

What motivates, justifies, gives rise to the differences between the Gumbel, Fréchet, and Weibull distributions? Glen_b's comment indicates that they are distributions for extreme values generated by ...
0
votes
0answers
29 views

How to model zero-inflated continuous response using categorical predictors - preferably resulting in multiplicative parameters

I'm having trouble finding a suitable model for predicting the AVG value (revenue in cents) of a single click on a product on a large e-commerce site. (assuming a click leading directly to a purchase ...
1
vote
1answer
62 views

Fitting a linear model with non gaussian noise

I am trying to evaluate the elasticity of prices of some goods. I am concerned about the gaussianity of the noise in the prices. With non gaussianity I am referring to the non existence of the ...
3
votes
1answer
88 views

expected lowest value of 10 normally distributed values

Consider 10 values that follow a standard normal distribution. What would you expect to be the lowest value? I tried to simulate this problem in R. I basically just simulated 100000 standard normal ...
2
votes
1answer
76 views

Fitting a probability distribution to non i.i.d. data? [closed]

I have temperature time series data that I have determined is not independently and identically distributed (from looking at the autocorrelation plots and Ljung-Box tests). However, I am still able ...
4
votes
1answer
78 views

Compare maxima of two Gaussian samples

Suppose $X$ and $Y$ are both normally distributed, with $X \sim \mathcal{N}(0,1)$ and $Y \sim \mathcal{N}(c,1),$ where $c > 0$. Consider $n$ independent draws of both $X$ and $Y$. As $n \rightarrow ...
3
votes
1answer
65 views

Distribution of Extreme Spread for n, sigma

Simple form provided by WHuber: What is the distribution of the diameter of n points in the plane drawn iid from a bivariate Normal distribution? (Diameter is the greatest distance among any pair of ...
0
votes
2answers
74 views

Joint cdf of extreme values

A die is rolled twice, $X_1$ : the minimum value to appear in the two rolls $X_2$ : the maximum I would like to derive $\ F_{X_1,X_2}(x_1,x_2)$. I know that that the CDF of $\ X_1 $ = $\ 1- ...
2
votes
1answer
79 views

Extreme value theory for count data

I am aware of extreme value theory for continuous distributions. I need to fit an extreme value distribution to the maximum observation of number of events on a day, per month. This seems to be the ...
4
votes
0answers
72 views

OLS robust to outliers

I am facing the following problem: I have a training sample and estimate a model on that training sample. My model is simply OLS: $y_t = a + \beta x_t + \varepsilon_t$. The model is estimated on ...
0
votes
0answers
52 views

What is loc parameter in GPD distribution in POT package for R?

I fitted gpd distribution by POT package available for R. Fitted object provide parameters shape and locations, but not parameter loc. I need it for evaluation of quantile function (qgpd(p, loc = 0, ...
6
votes
1answer
224 views

Two player dice game probability

$A$ and $B$ play a dice game where a player wins if their score is higher. $B$ wins if their score is equal. What is the probability of $A$ winning if both the players roll their dice $n$ times and ...
1
vote
1answer
120 views

Convergence in distribution of the maximum of a sequence of random variables

How to find the following: Let $X_1$, $X_2$, $X_3$,..., $X_n$, be i.i.d with chi-square distribution with one-degree of freedom. Find $a_n$ and $b_n$ such that $ a_n(\max_i X_i - b_n)$ converges in ...
7
votes
0answers
100 views

Tail bounds on Euclidean norm for uniform distribution on $\{-n,-(n-1),…,n-1,n\}^d$

What are known upper bounds on how often the Euclidean norm of a uniformly chosen element of $\:\{-n,~-(n-1),~...,~n-1,~n\}^d\:$ will be larger than a given threshold? I'm mainly interested in bounds ...
3
votes
0answers
50 views

Forming an unbiased estimator of the maximum of several parameters, given independent estimators of each parameter?

Say I have $K$ independent normals, $X_i \sim \mathcal{N}(\mu_i, \sigma_i)$ for $i = 1,...,K$. How can I form an unbiased estimator of $\max_i \mu_i$ using $X_i$'s?
1
vote
0answers
63 views

What is the meaning of McFaddens Axiom: Irrelevance of Alternative Set Effect?

On page 110 of McFadden,1973 - Conditional logit analysis of Qualitative Choice Behavior, Frontiers in Economics, ed Zarembka, New York: Academic Press, pp. 105-142 the following three Axioms are ...
2
votes
1answer
269 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
221 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
526 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 ...
3
votes
1answer
165 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
28 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 ...
1
vote
0answers
168 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
36 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
138 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
1k 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
254 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
63 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
43 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
190 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
153 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 ...
32
votes
9answers
1k 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
166 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
459 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
74 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
135 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
208 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
239 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
154 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
437 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
143 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
556 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 ...
0
votes
1answer
895 views

How to get expectation (E-value) for a dataset? [closed]

For an examination, scores for 10 students (all from class 4B) were obtained. I want to convert each score to E-value. If I understand correctly, to calculate E-value I have to determine an ...
2
votes
2answers
647 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
306 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 ...