All Questions
Tagged with minimum or extreme-value
196 questions with no upvoted or accepted answers
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Probability of random population value being higher than sample maximum
Considering a small sample size (n < 10) from a population, I'm trying to find how likely a random population value would be greater than the maximum of the sample.
Hoping ye could help me with ...
- 11
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1
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95
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Simulating Draws of Multivariate EV-Type Distribution
Let $\varepsilon = [\varepsilon_1,...,\varepsilon_J]$ be a random vector that we can partition into $K$ disjoint subvectors. $\varepsilon$ has this cdf:
\begin{equation} F(\varepsilon) = \exp \bigg[-\...
- 11
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117
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Group comparison for extreme value data: which method is suitable?
I have measured Gaussian curvature data of 3D objects from two different groups, A and B. I would like to find out whether the objects differ in curvature.
The distribution of data values for each ...
- 75
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196
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How is the minimum logarithmic loss calculated when initializing the XGBoost algorithm?
Suppose there are $5$ sample units, $2$ of which carry the feature $y=1$ to be predicted and three of which carry the feature $y=0$. So, $2$ are positive.
The XGBoost algorithm initializes with
$\...
- 11
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41
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How to compare frequencies of categorical variable with 3 possible values
There is one variable which can get one of 3 values and one sample. Lets assume values are A, B, C and frequencies are x, y, and z. How could I find if x > max(y,z), statistically significant? Or, in ...
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174
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Cumulative Probability Distribution of Maximum and 2nd from Maximum of 4 Variables
I understand that the cumulative probability distribution cum(x) of the maximum of 2 variables x1 and x2 with probability distribution p1(x1) and p2(x2) is the product of the two cumulative ...
- 389
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65
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Determine maxima and minima of fitted GAMM smooth
I have been using gamm4 to model the daily activity pattern of a certain behavior as a binomial response (whether the behavior occurs or not for each hour of the day). I am comparing the daily ...
- 41
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22
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Distribution of extremes of measurments considering repeated measures
I'm working with measurements for a large sample set and need to quantify the expected extremes. The measurements obviously have some degree of random noise simply in the measurement itself (for the ...
- 1,170
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371
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Statistics of Extremes: Fitting the GEV distribution with MLE vs L-moments
I created a synthetic series that is supposed to simulate a series of peak discharges in blocks of years in arid catchments. The magnitudes were simulated via the Lnorm dist.:
...
- 123
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551
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return level in non-stationary case using GPD (POT approach)
I'm doing some extreme value analysis, specifically, using a POT-approach and I'm trying to add some covariates to model excesses. Since I'm quite new in extremes, I'd like to ask for some help to ...
- 171
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272
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What is the most efficient implementation of the min-k-cut algorithm?
Simple question, I'd like to apply min-k-cut algorithm on a graph to partition the graph in k clusters by minimizing the sum of edges cut during the formation of clusters.
In my case I already know k ...
- 949
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364
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Normalising constant of the Gumbel in extreme value theory
Well known facts in extreme value theory:
Let $\{X_i\}_{\forall i \in \{1,...,n\}}$ be i.i.d. random variables with cdf $F$. If there exists $\{a_n\}_{n\in \mathbb{N}}>0$, and $\{b_n\}_{n\in \...
- 935
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35
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Error estimate for the position of a maximum given data
I posted the following question on Physics SE (here), but was told it might be better placed on Cross Validated.
Alright, so I am not sure what terminology easily describes this, but I have an excel ...
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33
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Compare maxima of two Bernouilli experiments
I am looking at the following question -- which has already been solved for the case of Gaussian samples Compare maxima of two Gaussian samples but I am unable to find a similar answer for the ...
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76
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Fitting a distribution to random variable in R when the data is available for minimum of those random variables
I am new in R. I have the following problem:
I have a dataset which presents the minimum of a set of n random variables (x1, x2,..., xn).
The formula is Min(x1, x2,...,xn) = 1-(1-F(x))^n.
It can be ...
- 11
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88
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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
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40
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How can I show that R^2 in multiple linear regression is maximum of corr(y,Xbeta)?
let
$Y=X\beta +\epsilon, \ \epsilon \sim N(0,\sigma^2 I_n)$,
(Y: nx1 vector, X: nxp matrix, beta:px1 vector)
assume that both $Y$ and $X$ are centered, so that the sum of them becomes 0.
How can I ...
- 467
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44
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Relationship between expected minimum as sample size increased
Suppose I have $N$ random variables $X_i$, $i = 1, \dots, N$. I am interested in the quantity
$$ A = \mathbb E \left[\min_{i=1, \dots, N} X_i \right]. $$
Now suppose I take a subset $S \subset \{1, \...
- 323
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1
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94
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Simple probability question (similar to birthday paradox)
If $x$ objects are randomly distributed to $n$ groups, what is the formula for working out how big $x$ needs to be for the probability that at least one of the groups gets an amount $y$ (or larger) to ...
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64
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What are some of the methods for constrained maximization?
This question is related to a question that I asked earlier. Since I am not able to decipher the algorithm in the original question, I would like to know whether there are other algorithms that can ...
- 629
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107
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Constrained Maximization Algorithm with Linear Contours
The Original Problem
Let $M(X)$ be a function of a multivariate random variable $X$ with probability density function $f_X(X)$. Given a small positive real number $\alpha$, find $m_{\alpha}$ such ...
- 629
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61
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How to test proportion against 1 - null hypothesis: H0: p=1
My research question:
I have a data set with good observations and bad observations and have to estimate if all observations are good in the population with 99% confidence.
My suggested method:
My ...
- 977
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202
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How to calculate growth rates up and down from a local maxima?
Problem: I am currently doing my Msc-thesis on rodent population dynamics. One of my aims is look at symmetry in oscillation topography. For this I want to calculate the growth rates up and down from ...
- 11
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46
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Probability that the Maximum of Many Normal Draws from Multiple Classes is of one Class
Given a set of $N=n_i+n_j+n_k$ draws from distributions $N(\mu_i,\sigma_i^2), N(\mu_j,\sigma_j^2), N(\mu_k,\sigma_k^2)$, what is the probability that the maximum drawn value was from distribution $i,j,...
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208
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Predicting risk of rare event occurring
Let's say I have a dataset containing a list of car accidents and associated information (e.g. weather, driver info, car state etc.).
Let's assume I know the number of cars on the road and the ...
- 103
1
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0
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308
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Could the sum of two normally distributed random variables be a GEV distribution?
I'm playing with Matlab, I have got a test statistic $T$ wich is of the form :
$$T(x)=\sum_{i=1}^{n}f_{i}(x)+\sum_{i=1}^{n}g_{i}(x)+c $$
Where $f$ and $g$ are functions of the observations $x$, $n$ is ...
- 902
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19
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Good predictive models for a linear minimum bound?
Are there any good predictive models for a pattern like the left plot of the first figure? I'm trying to predict how long a file transfer takes (in seconds) according to its package size (in bytes). I'...
- 379
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537
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which percentiles can be used to better describe the tail distribution
I understand that the extreme value distribution is concerned about the density of the tail which describes the losses if I am not wrong.
In such a case which part of the density(expressed as ...
- 153
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322
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Weibull, Gumbell and Extreme Value: from mean and variance to shape, scale and location parameter
I need to sample random numbers from Weibull, Gumbel and Generalized extreme value distributions. Of all of these distributions I know mean and variance. My question is: how can I determine these ...
- 253
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53
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Cov(y,z)? when z=min(Y)
For independently distributed normal random variables $y_i$ ~ $N(\mu_i, \sigma_i ^2 )$
Let $z =$ min$(Y) $, where $Y=${$y_1,y_2,y_3...y_n$}.
How to calculate cov$(y_j,z)$ ?
I tried to calculate it ...
- 11
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800
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Test extreme value distribution in Logit Model
Suppose I have a Logit regression with error term.
How to test the error term follows an extreme value distribution?
I check Logistic Regression in Wikipedia
it says
The choice of the type-1 ...
- 149
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26
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Get level set from 3D dataset obtained exploring a 2D space parameter
I am exploring a 2 parameter space performing simulations. As a result I get a surface as a function of these 2 parameters. I know this is probably simple but I don't know how to look for it.
Now I ...
- 111
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56
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relationship between rapidly varying tails and relatively stable distributions
Suppose a random variable X has cdf $F$ has rapidly varying tail $\overline{F} =1-F$, such that:
$$
\lim_{x \to \infty} \frac{\overline{F}(x\lambda)}{\overline{F}(x)}= 0
$$
if $\lambda >1$, and $\...
- 1,531
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275
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Confidence interval for maximum value in velocity time series
I have a time series of velocity values, which is structured into two periods. The first period describes the baseline velocity ("pre"). At the beginning of the second period ("post"), a stimulus is ...
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294
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Standard deviation comparison for splitting clusters in ISODATA
I am currently implementing the ISODATA algorithm and I am new to cluster analysis as I just learnt about it. I got stuck at the step which I need to compute the standard deviation of each cluster, ...
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355
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How to determine how many simulations to run, in order to illustrate "extreme-valued statistics"?
As an engineer trying to learn statistics, I wonder if someone could please recommend references / a statistical method that may assist with determining the number of simulations that need to be ...
- 11
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124
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Finding a global minimum of non-convex quasi-smooth function that is costly to evaluate
I have a bounded non-convex function in 10-dimensional space. The function is quasi-smooth, you can imagine a histogram, here is an illustration, it just shows the idea and not related to my ...
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325
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Certainty estimate for prediction of largest of several converging variables
Problem
I want to have an estimate for the certainty which of several (3-4) variables is the variable with the largest value, given some sample values which should eventually converge to different ...
- 1,034
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166
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Comparing min and max estimates
What is the most appropriate way to compare two groups of data in which, rather than a single value for each observation, we have two values per subject - a minimum and maximum value?
Basically, one ...
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204
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Is margin of error truly valid at extreme proportions? Such as 1% agreement, mere traces of data
Survey margin of error contracts as the proportions become more extreme. Its validity and applicability in such cases has always concerned me, but I suppose much depends on the context.
Where we have ...
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Mode of Joint Posterior - Maximization Problems
I have a problem whereby I get two different answers if I try to maximize a function.
let
$ \begin{bmatrix} Y_{o}\\ Y_{a} \end{bmatrix}|\phi\sim N (0,\phi^{-1}A^{-1}) $
$\pi(\phi)=\frac{1}{\phi}$,
...
- 121
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99
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Fitting of bivariate data to a self-defined probability density function
I have a bivariate set of data points which I want to fit to a self-defined distribution (i.e. not standard normal or chi-square or like that, a different, let's say "new" density function). I would ...
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165
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Find trendline for minimum (not mean) values in distribution
I would like to perform something like a linear regression on my distribution of data, but I'm interested in a trendline that estimates the minimum, not mean, value for each time bin. I'd like to do ...
- 125
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171
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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 ...
- 1,113
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501
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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 ...
- 131
1
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129
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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 $x$, ...
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Linearity of and pointwise equality in expectation of min() function
Consider the expressions $f = c + s*E[min(a/s, X)]$ and $g = E[min(c + a, c+sX)]$ where
c >= 0
0 < s <= 1
a >= 0
X ~ Poisson($\lambda$/s)
I'd like to think that $f = g$, reasoning as ...
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36
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Fitting a regression line which passes through the anchor point
In our setting, we have data $X_1, \ldots, X_n$, which can be ordered as $X_{1,n}\leq X_{2,n}\leq \ldots \leq X_{n,n}$ and we have the points $(-\log (1-\frac{i}{n+1}), X_{i,n})$ for $i=1,\ldots,n$.
...
- 656
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17
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Declustering impact, stationarity and discretization
I have a seasonal time series, and I am considering declustering (before any other preprocessing steps) it using runs declustering. If I observe an extremal index of 1, can I claim that my data is i.i....
- 1
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0
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55
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Does the mean of the maxima of a set of distributions converge?
This question is related to a recent one I posted. In that question I ask what statistic might best represent the central tendency of the true discrete distribution of a property for a sample for ...
- 165