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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49 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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52 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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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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22 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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57 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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29 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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19 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
545 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
56 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
37 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
72 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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24 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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30 views

Regression for long tailed time series events

I have a set of values which are a time series and follow a long tailed skewed distribution. I would like to understand what the best method might be to predict the next value in the series. Do the ...
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1answer
96 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
252 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
83 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
91 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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138 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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27 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
210 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
86 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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400 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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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
80 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
68 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
3k 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, ...
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1answer
272 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
248 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
193 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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1k 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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76 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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29 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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81 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
71 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
167 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
43 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
168 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
55 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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279 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
494 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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458 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
463 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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92 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
66 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 -...
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262 views

Relationship between the length of the whiskers and the tails of a population in boxplot

Why in the boxplots long whiskers are associated with a heavy tailed distribution and short whiskers are associated with light tailed distributions populations?
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1answer
3k views

Difference between long tail and short tail distribution?

I want to understand the difference between these distribution types. What is the difference between a long and short-tailed distribution?
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130 views

how to choose a transformation for left heavy tailed data due to arbitrary upper limit imposed by experimenter?

I have two vectors that look like this: I would like to make a significance test on the paired differences between the two vectors, as well as measure association. The process of data generation is "...
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1answer
108 views

Why is it assumed by default that distributions in nature satisfy the CLT?

It is inherently impossible to know the probability distributions of random variables we might encounter in the "wild" -- that is the reason why researchers have to take samples. However, since the ...
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1answer
34 views

Are the family of stable distributions differentiable everywhere on the real line?

Are stable distributions smooth enough for each index of stability $\alpha$ between 0 and 2, and skewness parameter $\beta$ between 0 and 1? Where there any papers that mention this?