All Questions
774 questions
1
vote
1
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75
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Which ones of $n$ random variables have the largest mean (non-parametric way)?
Let us have $n$ random, mutually independent variables $X_1,X_2,\dots,X_n$. Let us have some samples of them such as $x_{i,j}$ where $i=1,\dots,n$. I want to know the maximal variable(s) based on ...
- 2,846
5
votes
2
answers
1k
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Calculating the distribution of maximal value of $n$ draws from a normal distribution [duplicate]
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
$E(\max|\...
- 505
3
votes
0
answers
107
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 $X+Y+Z$ ...
- 328
1
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0
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325
views
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
1
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0
answers
164
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Given n iid Pareto distributed random variables, find the UMP one sided test of the first moment
Given $X_1,...,X_n$ ($n\geq 2$) are iid and each have density:
$f_X(x) = \frac{c^\theta \theta}{x^{1+\theta}}\mathbb{1}(x> c)$ for known $c$ and $\theta > 1$
then we can easily find the first ...
- 87
3
votes
0
answers
1k
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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 distributions,...
- 951
1
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0
answers
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,...
- 11
1
vote
0
answers
53
views
Mean & Variance after applying a Maximum function n-times [closed]
I am trying to solve a statistics problem with very little statistics theory. I can determine a solution to my problem by writing a simulation program, but I really need to have the proper formula ...
- 11
3
votes
0
answers
818
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Random Forest Regression - Coping with extreme values [duplicate]
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 / $\text{km}^2$. I have a database of around 24000 points ($\text{...
- 3,875
0
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0
answers
72
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two-parameter Pareto distribution with known A [duplicate]
I am trying to solve the following problem. Any help would be great:
Scores are distributed as a two-parameter Pareto distribution with a=3
Scores for 3 groups are as follows:
Group A has expected ...
- 11
2
votes
0
answers
29
views
Problem computing population quantiles with survey micro data
All the major federal surveys come (American Community Survey, Current Population Survey, others) come with survey weights, such that the individual household observations times the population weights ...
- 3,247
0
votes
1
answer
57
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modelling minimal threshold line
I am examining the relationship between population density and incidence of a disease (calculate by count of number of cases / population) in a geographical area sub-divided into adjoining districts.
...
3
votes
2
answers
2k
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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.
...
- 31
1
vote
1
answer
308
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Pearson 5/Inverse Gamma/ Double Pareto
My current research deals with landslide size frequency distribution which has been fit to a three-parameter inverse gamma function and a double Pareto function by previous researchers. I am trained ...
- 11
1
vote
1
answer
41
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Parameters of response distribution , response expectations
What is the meaning of this sentence?
...
- 13
1
vote
0
answers
329
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expected shortfall and value-at-risk [closed]
I once read a R example of computing Value-at-Risk and expected shortfall as follows
...
- 3,089
2
votes
0
answers
589
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Convergence in Probability of the minimum
This is a homework question. I think I have the correct answer, but I am not sure. Also, the wording sounds very awkward. Is there a better way to show this (or better way to word this)?
Let $X_1,\...
- 10.2k
2
votes
1
answer
324
views
One sample $t$-test with range values
I need to compare an average value for an experimental group ($n=5$) with a reference value given by legislation.
But this reference value in given as [min - max] range.
Do I have to compare my ...
- 23
5
votes
1
answer
169
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 ...
- 1,176
2
votes
1
answer
265
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KL divergence minimisation equation
I am looking at some literature on KL divergence minimisation and am having trouble understanding the derivation of the second order moment. So, if we have a distribution from the exponential family, ...
- 4,730
7
votes
1
answer
2k
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Tangency portfolio in R
I am trying to solve for an efficient portfolio in R. How do I translate my constraints for a tangency point for 2 risky asset portfolio, and a given risk free rate to R solve.QP function? So ...
- 2,799
3
votes
1
answer
1k
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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 ...
- 286
2
votes
1
answer
131
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Asymptotic distribution of a recursive statistic
I have a (time series related) test statistic which is asymptotically normal. I would like to know what is the asymptotic distribution of its maximal value obtained by a recursive estimation.
For ...
- 23
3
votes
1
answer
406
views
How to use the Pareto distribution in fitting survival curves?
I have a series of numbers, which are some survival probabilities that form a decaying curve. I would like to fit them with a "Pareto" distribution. I expect to have a smooth fitted curve, thus I can ...
- 275
2
votes
1
answer
266
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 ...
- 958
5
votes
1
answer
313
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 ...
- 153
1
vote
0
answers
211
views
Evaluate goodness-of-fit of estimation of Pareto-like distribution
I would like to evaluate the goodness-of-fit of the following (Pareto-like) distribution:
$$
f(r) = \sigma \centerdot r^{-\rho}
$$
The function estimates the population of cities given the rank $r$ in ...
- 53
2
votes
0
answers
69
views
How to extract 20-80 relations from data (Pareto principle)?
There are certain input-output processes that display a "20-80 relation". That is, given Y depending on X, there are subsets of X consisting 20% of the input set that generate 80% of the output. For ...
- 21
2
votes
2
answers
618
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 ...
- 123
2
votes
1
answer
141
views
Why is it that it is self-defeating to use the posterior mode as the bayes estimator in this case?
I am reading through an applied statistics book and in it, it makes a very luminous statement for a posterior case where the likelihood was taken from $X_1,...,X_n$ iid random variables from a ...
- 2,107
3
votes
2
answers
341
views
Probability of a random variable to be the largest among others
Let us have $N$ random variables generated by uniform distribution. That is, $$u_i \sim \mathcal{U}(0,1),\quad i=1,\ldots,N$$.
What is the probability of $u_N$ being the largest? I.e., how can I ...
- 75
2
votes
0
answers
89
views
Extreme Value Theory Data Scaling
I have a data set available of almost thirty years of data, with for each month the number of occurrences of a certain event and the total number in the set available.
What I would like to compute is ...
- 35
1
vote
1
answer
23
views
Assign each sample in B to each element of a matrix A
I've measured the distance between 100 brain regions and 5 "core" brain regions. This led me to a 100x5 matrix (A) of empirical distances.
Now, I have a second 100x5 matrix (B), where the distances ...
- 472
1
vote
0
answers
53
views
Is the variability index valid for the Pareto distribution
The Pareto distribution is defined from the CDF:
$$
F^{-1}(p) = \frac{b}{(1 − p)^{1/a}},\ 0 < p < 1,
$$
where, $b$ is the scale parameter and $a$ is the shape parameter.
In the Gaussian ...
- 11
1
vote
0
answers
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
1
vote
0
answers
501
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 ...
- 131
0
votes
1
answer
186
views
Expectation of the Pareto distribution [closed]
I would like to know if my understanding of the following is correct. This has been tripping me up for a long time now.
Compute $\lim_{x\rightarrow \infty}x^{1-\beta}$.
This is part of a homework ...
user30602
7
votes
1
answer
449
views
How can I apply a Pareto tail to a truncated distribution?
Many income surveys (especially older ones) truncate key variables, such as household income, at some arbitrary point, to protect confidentiality. This point changes over time. This reduces inequality ...
- 71
0
votes
0
answers
20
views
New question based on an existing question on Minimum and Maximum of N(0,1) [duplicate]
This question is an additional question to the given posted here: Variance of Minimum and Maximum of 2 iid Normal
Let $X, Y$ be independent $N(0,1)$ and let $M=Max(X,Y)$. In the previous problem, ...
- 1,347
1
vote
0
answers
65
views
Extreme value theory？ [closed]
I am studying probability and finding hard to understand the following equation.
$Pr[P_i \leq \min\{P_s;s \neq i\}]=\int_0^\infty \underset{s\neq i}{\prod}[1-G_s(p)] \, dG_i(p)$
where $P_i$ are ...
- 19
3
votes
0
answers
352
views
Correct variance for minimum detectable difference
I have a question regarding variance, paired testing and minimum detectable difference (MDD).
Paired samples:
$$
MDD (δ) = \sqrt{ \frac{σ^2}{n} (t_{(α/2,n-1)} + t_{(1-β, n-1)})}
$$
I have a set of ...
- 31
1
vote
0
answers
124
views
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 ...
- 11
0
votes
0
answers
46
views
Subset of Pareto/powerlaw distribution
Given a set of random data generated using pareto-distribution, how can I get X% of this random data without losing pareto-distribution.
In other words, how to select a subset of pareto-distribution ...
- 121
1
vote
1
answer
70
views
Exclude Some samples for calculating CDF
I am calculating the asymptotic cumulative distribution of $M_n = \max(X_1,X_2,\dots,X_N)$. My problem is $X_1,X_2,\dots X_p$ and $X_k,X_{k+1},\dots,X_N$ have non identical CDF for $p<<k$ and $p&...
- 301
2
votes
0
answers
49
views
Is there a distribution that covers Pareto's law?
Is there a distribution where (for example) 80% of the results come from 20% of the inputs? (i.e. Pareto's law). Hmm... there's a tag for Pareto Distribution ... is that the answer?
- 121
7
votes
1
answer
125
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Measurement error in maximum counts
I'm familiar with the concept of a mean value of data and the variation around the mean. Is it possible to quantify variation around maximum values?
For example, take the below data collected across ...
- 14.6k
0
votes
2
answers
303
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Trouble using pareto levy stable distribution software [closed]
I'm using an arcane free program off the internet called "stable.exe" trying to fit a stable distribution curve to a dataset, but I'm having trouble entering the dataset file into the program. When ...
- 515
1
vote
0
answers
56
views
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
1
vote
0
answers
15
views
How to write the set of indexes of Pareto optimal reward set in formal methods
I denote that a reward vector of an item $a$ as $r_a$. Say there is a set of items denoted as $A_t$. I want to get a set $A^\prime_t$ of items from $A_t$ that has non-dominated reward vectors. For a ...
- 123
2
votes
0
answers
30
views
Optimizing while collecting data - optimization in a real world problem
I want to conduct a soil analysis using a different mix of let says Nutrition A, Nutrition B and Nutrition C.
Since I can put for each nutrition multiple values, I cannot try out all the possible ...
- 547