Questions tagged [heavy-tailed]
Heavy-tailed distributions have tails that are not exponentially bounded (eg, log-normal & Pareto [heavy right tail], & t [both]). For general questions about fat tails, use the [kurtosis] tag.
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Family=scat in mgcv not behaving as expected
I am analysing the eye-tracking data of an experiment in psycholinguistics I ran some time ago, and after fitting a model that captures the data pretty well, I ran a number of model checks and found ...
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1answer
19 views
Which is the right measure of dispersion to be used as a proxy for risk for a fat tail distribution?
Which is the right measure of dispersion to be used as a proxy for risk for a fat tail distribution ? Standard Deviation, Mean deviation, Value at risk, what else?
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How to measure the level of tail dependence in copula?
In the Clayton copula below, we see that there is stronger lower tail dependence (bottom left corner of Clayton) than upper tail dependence (upper right corner) because the pseudo-observation pairs in ...
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1answer
28 views
A tail bound for an unknown distribution via sampling
I know that many results exist for making an argument about the tail of a distribution, i.e., for a random variable $X$, one can find a bound $\epsilon$ such that $\Pr[X \geq a]<\epsilon$. Some ...
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4answers
577 views
In comparison with a standard gaussian random variable, does a distribution with heavy tails have higher kurtosis?
Under a standard gaussian distribution (mean 0 and variance 1), the kurtosis is $3$. Compared to a heavy tail distribution, is the kurtosis normally larger or smaller?
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3answers
190 views
Sampling from heavy vs light tailed distribution
I am having some issue understanding the behavior of such distributions when generating random numbers.
I was under the impression that heavy tailed distributions have "heavier" tails, so ...
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1answer
66 views
Short tailed/Long tailed distributions and their effects on p-value interpretation when assuming normality
Can anyone offer better insight into the comparison of how p-values for hypothesis tests are affected when your distribution is short/long tailed but we assume it is normally distributed? I'm ...
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0answers
56 views
Heteroskedasticity tests: heavy-tailedness of squared estimated errors
I have a time series model and obtain the following distribution of estimated errors:
I suspect that the errors are heteroscedastic in the sense that their variance depends on the level of one or ...
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0answers
79 views
How do we call a more extreme case of fat tails than a power law?
According to Wikipedia the most extreme case of a fat tail follows a power law:
The most extreme case of a fat tail is given by a distribution whose tail decays like a power law.
That is, if the ...
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0answers
26 views
Can someone please explain “L1 Regularization is inefficient when the errors in data have heavy tail distribution”
I was reading into L0, L1, and L2 regularization and I found this research paper. On page 2, paragraph 3 it mentions the line
L1 Regularization is inefficient when the errors in data have heavy ...
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0answers
111 views
linear mixed effect model with symmetrical heavy tailed errors distribution
I am using the Lmer function from the lmerTest in R to test the significant of fixed effects ...
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0answers
44 views
GAM scaled t family for heavy tailed distributions
I have some heavy tailed data I wish to model using the mgcv package in R with a t-distribution.
Reproducible example:
...
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20 views
Appropriate Data Analysis when Criterion has Heavy-Tailed Distribution
I have a data set where my independent variables (i.e., personality assessment scores) are continuous and follow a normal distribution. The criterion, sales performance, is heavy-tailed and follows a ...
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2answers
939 views
Regression with heavy-tailed response variable
I have a response variable that is unbounded and continuous, but has heavier tails and violates some of the assumptions of normality (see plots below).
This variable represents selection coefficients ...
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1answer
74 views
Appropriate to fit lognormal model to data with heavy tail?
I am attempting to standardize recreational fishery CPUE data. I am using a delta approach, with a binomial model fit to the presence/absence data and a lognormal model fit to the positive ...
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1answer
69 views
Connection between subgaussian/subexponential and exponential family
I am wondering if there is any relationship between subgaussian/subexponential with (one parameter) exponential family.
In particular, is there any sub-family density that belongs to both ...
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1answer
87 views
Want to know the differences between exponential and heavy-tailed distributions in terms of first and third quartiles
What are the differences between exponential and heavy-tailed distributions, please illustrate this difference by explaining how well the first and 3rd quartiles describe them.
I know what are ...
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0answers
53 views
How are the signs of the loadings in ICA interpreted?
In my novice understanding of ICA, we generate two matrices: a source matrix, which describes the contribution of variables to the independent components (analogous to loadings in PCA..?) and the ...
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1answer
141 views
Correlation of heavy tailed variables
I have two heavy-tailed random variables and want to know if they are correlated. While I only have estimates for the tail exponent, it is in a ballpark so that variance would normally not exist. The ...
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2answers
352 views
Bootstrap confidence interval on heavy tailed distribution
I read from Wikipedia:
... if one performs a naive bootstrap
on the sample mean when the underlying population lacks a finite
variance (for example, a power law distribution), then the ...
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2answers
111 views
Identifying the tail of a heavy tailed distribution [closed]
I have several distributions with a heavy right hand tail as shown below.
I am not interested in analyzing the tail of this distribution. Is there any official definition on where a tail begins on a ...
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1answer
114 views
Are the skew-normal distribution and the skew-Cauchy distribution heavy-tailed?
I think the title is self-explanatory. I understand that the skewness and the tail behavior of some distribution are completely unrelated as any symmetric distribution will have a skewness of zero ...
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0answers
151 views
When I fit my data with GEV, I got positive parameter, but when I fit it with GPD, I got negative parameter?
My data is the total annual precipitation in Australia. My purpose is to observe the extreme precipitation on the right end tail. When I fit my data with Generalized Extreme Value, I got positive ...
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29 views
How can Pareto(alpha = 5, x_min = 2) be heavy-tailed where alpha is the shape parameter or the tail index?
Point 1 : It's known that, usually, when the tail-index (alpha) is between 0 and 2, of a certain data set, the distribution is considered as heavy-tailed.
Point 2 : It's know that Pareto ...
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1answer
254 views
Distribution of the inverse square of a non-standard normal random variable multiplied by a constant
It's a somewhat complicated situation and sorry about my phrasing, but it's my first time here. Suppose I have random normal variable $X$ ~ $N( \mu, \sigma^2)$, which represents some true effect(s). ...
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1answer
102 views
Alternative to Chow test in the case of heavy tailed residual distribution
I would like to check if two subpopulations of my data have the same parameters in a model. Model 1 is based on subpopulation 1 and Model 2 is based on subpopulation 2.
Model 1: $y=x^\alpha + \...
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2answers
419 views
Quantifying dependence of Cauchy random variables
Given two Cauchy random variables $\theta_1 \sim \mathrm{Cauchy}(x_0^{(1)}, \gamma^{(1)})$ and $\theta_2 \sim \mathrm{Cauchy}(x_0^{(2)}, \gamma^{(2)})$. That are not independent. The dependence ...
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3answers
127 views
What does it mean to say that $X_1, X_2$ have a “common” Normal distribution?
An exercise question asks
Let $X_1, X_2$ be rvs having a common Normal distribution $N(0,1)$ with $\operatorname{Corr}(X_1, X_2) = \rho$. Calculate the coefficient of upper tail-dependence for all $...
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1answer
87 views
need explanation about the exponent parameter s in zipf distribution
I need to model the popularity of some requested files from a library with Zipf distribution and I want to simulate it in MATLAB. I don't know what's the effect of parameter s on my result. for ...
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1answer
73 views
How can I derive the function curve from a histogram of observed data
I'm analysing some datasets that produce heavy tailed data when plotted as a histogram. My initial goal was to attempt to fit a known distribution to my dataset. Thereafter I use to the properties of ...
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2answers
4k views
Formal definition of the qqline used in a Q-Q plot
I'm doing some distribution fitting work and I'm looking at Q-Q plots and how they can be used visually to interpret goodness of fit.
My data is heavy-tailed so I am looking at Weibull, log-normal, ...
3
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1answer
285 views
Is the truncated power law a heavy-tailed distribution?
A heavy-tailed distribution is often defined as a distribution with a tail that is not exponentially bounded.
A truncated power law (or power law with exponential cut-off) is a distribution that ...
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1answer
289 views
Transform Heavy right tailed data
I am clustering (K-MEANS) a data 1.7million observations, which displays a heavy-tailed distribution when examined by plot. What is the best transformation to correct it. does log can handle this?
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1answer
211 views
A question about qqplot
This is my qq plot :
Its concave-convex curve so it indicates light tails. But my mean excess plot :
is increases which means the tail of the distribution of my data is heavy-tailed.
I don't ...
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0answers
2k views
In a left skewed distribution, how can the range where 95% data lies?
In a simulation that I ran, I have the following graph as a result. How can I find the 95% confidence interval (i.e. the range where 95% of data lies for me).
Since I am not expert in stats, please do ...
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1answer
55 views
Decomposition of the probability of the sum
I cannot understand how is gotten the following decomposition.
Supposing that $X_1,...,X_n$ random variables i.i.d with heavy tailed distribution $S_n=\sum_{i=1}^nX_i$
In the article that I m ...
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103 views
Determining the distribution of data
Hi, I am a student learning financial modelling. I would like some help in determining the distribution of the data given the plots above. I am reluctant to assume normal distribution of the data due ...
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0answers
31 views
Determining the number of observations within the tail of a given distribution
I am wondering how to determine the number of observations that fall within the tail of a distribution. I am reading a paper and the authors use the assumption that 50 observations need to fall into ...
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0answers
86 views
Left “tail” of one-tailed distributions
I think of the "tail" of a probability distribution as the behavior of its PDF $f(x)$ as $x\rightarrow +\infty$. For some PDFs with complicated expressions, it is sometimes easy to study their ...
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3answers
77 views
If the best-fitting distribution has infinite variance, should low observed variance be troubling?
Suppose you have observations which, over the observed range of outcomes, are well-fitted by some distribution like the Pareto that, for certain parameter values, has a an infinite variance. For ...
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1answer
207 views
Does the normality assumption hold? Is this an outlier?
I am trying to fit a multiple linear regression (OLS) model with IPO underpricing as dependent variable. As part of my master thesis I would like to analyze the effect of venture capital ...
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1answer
44 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}, ...
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2answers
186 views
Regression: zeros in heavy-tailed independent variable from quantization
This question is about handling zeros in an independent variable for a regression.
In particular, the zeros are not missing data or true zeros, but occur because of quantization. As a concrete ...
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0answers
56 views
Rigorous threshold determination for heavy-tailed data?
Overview: I'm trying to design a change-point detection system for univariate, non-normal, skewed, heavy-tailed data that I believe is generated by a stable random process (i.e. stable-distributed ...
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0answers
302 views
Motivation behind the definition of a heavy-tailed distributions
The current Wikipedia definition is
The distribution of a random variable $X$ with distribution function $F$ is said to have a heavy (right) tail if the moment generating function of $F,$ $MF(t),$ ...
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1answer
528 views
Visual fitting of tails of density plots on log scale (R)
Density plots are useful in confirming the fit of a distribution or assessing which distribution to try in order to give the best fit. However, when looking at the tails on log scales, especially for ...
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461 views
tail dependence calculation
If I have the tail dependence value calculated using Joe (1997) in fact $R$ gives the result for any family copula. Using Caillault and Guegan method called "naive" what are the main differences? Why ...
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2answers
512 views
inferring heavy-tail distribution from finite sample of histogram data
I have some data in the form of bins and counts. Here is one complete non-truncated example:
...
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0answers
96 views
Parametric modelling of survival data: when there is no event in a long tail, is there information?
I have a survival analysis question. Let's take a look at the below curve:
For the red curve, there are no more events after 48 months. For the black curve, there are no more events after 60-ish ...
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1answer
67 views
On the existence of a heavy tailed c.d.f. given a condition based on the CLT
My question is about the existance of a heavy tailed distribution $F$ such that: given two i.i.d. samples $\{X_1,\ldots,X_n\}$ and $\{Y_1,\ldots,Y_n\}$, from $F$, we have
$$\sqrt{n}\frac{\hat{\mu}_X -...
