All Questions
774 questions
2
votes
0
answers
135
views
Interpret the result of a fitted non-stationary Gumbel model
I have a dataset on wildfires that I fitted to a Gumbel distribution with a set of covariates (using the gevrFit function in the eva package in R). The result of ...
- 21
5
votes
1
answer
195
views
Lomax distributions - Kullback Leibler divergence
Does anyone know of a reference for an expression for the Kullback-Leibler divergence between two Lomax (Pareto II) distributions? Not really worried which way the Lomax is parameterized.
- 51
3
votes
2
answers
26k
views
Given P(A) and P(B), what would be the minimum probability of the intersection?
Like if I was given a P(A) of .5 and a P(B) value of .4 how would I get the minimum of the P(A∩B)?
- 41
2
votes
1
answer
350
views
Expectation of two identical lognormal distributions
I would like to compute the conditional expectation (on an interval from $c$ to $\infty$) of the minimum of two log normal distributions.
Denote $X_1$, $X_2 \sim LN(0, \sigma)$, the associated ...
- 229
4
votes
1
answer
3k
views
Hypothesis testing for Pareto distributions
I wish to to some simple hypothesis testing of the form provided by T-Tests and ANOVA. However, my data is not normally distributed (it follows a Pareto distribution).
My understanding is that T-...
- 2,608
1
vote
0
answers
308
views
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
3
votes
1
answer
1k
views
Weighting observations and measurement uncertainty in bayes
I am working on using MCMC (via STAN) to estimate model parameters for a bunch of observations with measurement uncertainty. I'm having problems with weighting each observation, and have reduced the ...
- 203
5
votes
1
answer
755
views
Can an estimator of the mean of a distribution with no variance have a variance?
Suppose you have a sample from a distribution with a mean but no defined variance, like the Pareto with tail parameter between 1 and 2, or Student’s t with 2 degrees of freedom.
Can an unbiased ...
- 3,247
1
vote
0
answers
537
views
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
3
votes
2
answers
527
views
Probability of Unique Minimum (Discrete)
This is a discrete problem concerning integers.
If there are $n$ independent random variables $X_1,...,X_n$ that each take on a value from $\{1,...,x\}$ uniformly at random ($x$ distinct values), ...
- 133
5
votes
1
answer
3k
views
What do I need to consider when using the Hessian to compute 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 ...
- 958
0
votes
1
answer
191
views
How to find the maximum likelihood of this scenario occurring?
I have the equation: $ 0= 2.01106 - 0.00274(34.647+24.24a)-0.02059(45.647+21.122b)+1.37984(2.05-0.206c)-0.01176(10.588+11.963d)+0.00394(118.29-21.097e)-0.03552(92.17+2.855f)$
I have the above ...
- 103
1
vote
1
answer
39
views
How is this way of rewriting extreme-value problems a simplification?
This question is about pp. 370-374 of Harald Cramer's 1946 Mathematical Methods of Statistics. The author considers a more general question, but for simplicity let us focus on the question of:
...
- 6,479
5
votes
1
answer
2k
views
Truncated Pareto estimation
Given min and max values, how can I estimate shape parameter (tail index) of data generated by truncated pareto distribution ? I see a package tpareto but find no information on how to estimate tail ...
- 71
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
4
votes
1
answer
3k
views
Moments of the two-parameter generalized Pareto distribution (GPD) needed
In
this thread
the first two moments of the two-parameter GPD are given, where the distribution might be defined as
$G(y)= \begin{cases} 1-\left(1+ \frac{\xi y}{\beta} \right)^{-\frac{1}{\xi}} & ...
- 1,082
1
vote
1
answer
27k
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 ...
- 611
1
vote
1
answer
255
views
Need help finding an unbiased estimator [closed]
Suppose that the pdf for $T$ is exponentially distributed
$$f(x; θ) = \frac{1}
{θ}
e
^{−x/θ}
, 0 ≤ x < ∞$$.
Suppose we test n components and record the failure times $T_1, . . . , T_n$.
(a) Show ...
1
vote
0
answers
408
views
Estimate minimum values of the dependent variable [closed]
We know that linear regression estimates the expected mean value of a dependent variable, as a function of the independent variables.
I would like to know, however, if there is any theory about some ...
- 119
3
votes
1
answer
1k
views
Kolmogorov-Smirnov for Pareto distribution on sample
I want to use the Kolmogorov-Smirnov test to test if a sample is drawn from a Pareto distribution. Unfortunately, the only way to estimate the distribution's parameters is from the sample.
Does ...
- 53
1
vote
0
answers
235
views
Standard error of Pietra index with Pareto assumption
I am working on this problem of income distribution.
I am assuming that my income data $X_i$ is Pareto : $f(x_i;\alpha) = {\alpha \over x_0}({x_i \over x_0})^{-(\alpha + 1)}$
I found my MLE ...
- 770
3
votes
1
answer
962
views
How to find $\arg\max$ of a neural network?
Let's say I have a neural network $f$ that takes input $\vec x \in \mathbb {R}^n$ and produces output $f(\vec x) \in \mathbb{R}$.
How can I find $\hat x = \underset{\vec x}{\arg\max} \; f(\vec x)$?
- 3,132
1
vote
0
answers
202
views
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
11
votes
0
answers
1k
views
Hyperprior Noninformative Beta Binomial Model [closed]
I've been working through Gelman's Bayesian Data Analysis 3 text and have been trying to understand one of the hierarchical models revolving around rat tumors (Chapter 5). He uses a binomial model ...
- 111
10
votes
2
answers
11k
views
How to find when a graph reaches a peak and plateaus?
This may sound very basic, but I have this problem:
I've got a queue of data with a window size of 300. New data is added at one end, old values are removed from the other end.
I expect the queue ...
- 203
1
vote
1
answer
3k
views
How to calculate max/min scales on a scatter plot
I have 3 log scatter plots that I want to establish smooth maximum and minimum lines. What is the usual mathematical method to do that? (Image and Excel file links below.)
The black lines on the ...
- 39
1
vote
0
answers
360
views
How to estimate Pareto shape parameter with bayesian estimation?
I want to estimate the shape (alpha) parameter for a Pareto distribution. (We assume that we know the scale parameter =1 ).
The prior is alpha = 2 (and maybe we have always to assume a distribution ? ...
- 250
2
votes
0
answers
312
views
How to train a generalized extreme value model for anomaly detection?
Background
I am building an anomaly detection solution. So far I used the simple z-score (#std from mean) approach. The latter implicitly assumes an underlying stationary Gaussian model. However, the ...
- 461
0
votes
1
answer
176
views
How to regularize parameters across a 2D array
I'm attempting to fit a parameter (which will be a 2D array) to an array of data which corresponds to spatial locations (i.e. longitude/latitude). The parameter can vary from point to point but I want ...
- 103
4
votes
1
answer
563
views
joint probability distribution of $k \le n$ order statistics
For $X_i \sim$ iid random variables:
For $1\le r_1 < ..<r_k \le n$ integers, I am trying to find the joint pdf of:
$$
(X_{(r_1)},...,X_{(r_n)})
$$
where $X_{(r_1)}$ is the $r_1$th largest ...
- 1,531
2
votes
1
answer
55
views
A random variable $X$ on $(0,\infty)$ which behaves like Exp for small $x$ and Pareto for large $x$
Are there any examples of distributions which behave like Exponential for small values and like Pareto for large values.
$$\ln \mathbb{P}[X>x] \sim -\lambda x, \qquad \text{ for } x \text{ small}, ...
- 53
0
votes
0
answers
66
views
Training Neural Network at Decile Level
I have a simple feed forward neural network regression model that I'm training on customer data to predict their usage amount. The MAPE is above 50%. The data is heavily skewed and when I log ...
- 121
5
votes
1
answer
112
views
Distribution of $\dfrac{X_{i}}{\max X_{i}}$?
Suppose we have a sample of standard normal i.i.d. observations $X_{1}, X_{2}, \cdots ,X_{n}$, what can we say about the asymptotic distribution of $V_{i}$ and $W_{i}$, where:
$V_{i}=\dfrac{X_{i}}{\...
- 902
1
vote
1
answer
485
views
Parameter estimation problem: maximum likelihood [duplicate]
Suppose I have some observations $x_{1}, x_{2}, \dots, x_{n}$. I also have a probability density function with one unknown parameter $\theta$. I would like to find such $\theta$, which would give the ...
- 21
0
votes
1
answer
99
views
3-level hierarchical model and ferquentist approach
Could I use maximum likelihood method or any other frequenist method to estimate parameters for 3-level hierarchical model?
Is there any references help me in this case?
Thank you
- 11
0
votes
1
answer
2k
views
Calculating percentage difference between maximum and current value
I am having a set of calculations say variable x and a maximum value max(x). I want to calculate percentage difference of variable or observation xi from max(x).
What can be the most suitable ...
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
2
votes
1
answer
532
views
Calculation of confidence interval of a population parameter (the range)
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_{\text{dif}}:= P_{\text{max}}...
- 131
2
votes
2
answers
212
views
P(X<Y|Z=t) where Z=min(X,Y)
Lets X and Y be uniform random variable where $x \in [0,a]$ and $y \in [0,b]$ where a < b. We design $Z=\min(X,Y)$.
I know that the CDF of Z is $P(Z<z)=1-\frac{(a-z)(b-z)}{ab}$
And by ...
- 719
5
votes
1
answer
400
views
Properties of the minimum of several random variables
I've come across an interesting problem in my research that I don't quite know the answer to. Suppose I have a bunch of random variables:
$$ X_1, X_2, X_3, ... X_N $$
They are not identical but they ...
- 311
1
vote
1
answer
974
views
Generalized minimum chi-square estimators?
I need to implement the generalized minimum chi-square estimators (alternative to L-moments method and maximum likelihood estimate (MLE)) for estimate the parameters of the gamma distribution.
My ...
- 41
2
votes
1
answer
487
views
Help understanding successive maximization in step-down maxT algorithm
I am currently trying to better understand different permutation-based procedures for controlling FWER. Specifically, the minP/maxT procedures that are commonly used. One of the problems I am running ...
- 1,903
1
vote
1
answer
183
views
Tail equivalence for heavy-tailed data
Is it possible for a distribution $F(x)$ that has not a Pareto ($G(x)$) right tail equivalence to fit well heavy-tailed data?
That is, to have ${\lim_{x\rightarrow\infty}}\frac{1-F(x)}{1-G(x)}=0$ ...
- 113
3
votes
2
answers
1k
views
Given the location and scale parameters of a Gumbel distribution for variable X, how does one calculate the mean and variance of X^2?
I am working with predictive models for wind speeds, which have been given as Gumbel distributions. I need to convert the wind speeds to wind pressures using the formula:
$Pressure = Density * ...
- 31
0
votes
1
answer
179
views
Obtain the coordinates of one point (X1,Y1) where it is maximum the change of the curve [closed]
(source: biomedcentral.com)
Dear community,
I used a figure obtained from internet to illustrate what I would like to solve. Imagine this exponential regression curve.
How can I get the exact point of ...
- 473
3
votes
0
answers
85
views
An arithmetic mean preserves normal distributions, maximum preserves Frechet/Gumbel/Extreme Value distributions, but what about all other power means?
Let the $k$-power mean of two numbers $x$ and $y$ be defined as $M^k(x,y) = \left(\frac{x^k+y^k}{2}\right)^{1/k}$.
For the case $k=1$, we have that if $X,Y$ are independently normally distributed, ...
- 1,594
1
vote
0
answers
77
views
Quotient of Pareto and Gamma random variables
I cannot find an explicit formula for the quotient of a Pareto random variable divided by a Gamma random variable.
The only that I found is something like, for $P(X)$ pareto's like and $P(Y)$ Gamma's ...
- 11
4
votes
1
answer
590
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 ...
- 311
1
vote
0
answers
689
views
Posterior of alpha parameter (Shape) of Pareto Distribution
Im trying to generate the posterior distribution of $\alpha$ parameter of Pareto Distribution.
I did all the job correctly on paper, but when i go to implement in R i have some problems.I have a ...
- 253
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