Questions tagged [heavy-tailed]

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2
votes
1answer
566 views

How are errors terms calculated in GARCH model by rugarch package?

I am fitting a GARCH(1,1) model to the data and want to look at the innovation distribution. ...
2
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0answers
120 views

Predictive modeling of an complex panel of heavy-tailed data

I am struggling to develop a sensible strategy or protocol for the predictive modeling of a complex set of data. Apologies in advance for the indeterminate nature of some of this description but it’s ...
0
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2answers
802 views

Data transformation for heavy tailed data for mixed model use

I am trying to transform my data to meet assumptions of a mixed model (lme4). This is the qqplot for the data. I have tried the traditional transformations: log & square root.
4
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3answers
1k views

Are two asymptotic values enough to fail the test of normality?

Looking at this post I started to wonder about the gestalt interpretation of the QQ plots generated by qqnorm in R. Here's the plot to avoid having to go to the ...
6
votes
1answer
858 views

Bernstein's inequality for heavy-tailed random variables

It is known that for independent sub-exponential random variables, the following Bernstein-type inequality holds: \begin{align} \mathbb{P}\biggl(\biggl| \sum_{i=1}^N a_i X_i\biggr| >t \biggr) \...
10
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3answers
7k views

t-distribution having heavier tail than normal distribution

In my lecture notes it says, t-distribution looks like normal, though with slightly heavier tails. I understand why it would look normal (because of the Central Limit Theorem). But I am having ...
2
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1answer
49 views

Fitting upper and lower student-t separately

I'm doing some research on fitting marginal distributions to data, in particular distributions with a focus on heavy tails. In one report, albeit several years old, the authors suggested fitting a ...
6
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3answers
6k views

what is the meaning of 'tail' of kurtosis?

There are two kurtosis types : positive(leptokurtic) and negative(platykurtic). leptokurtic is heavy tailed, and platykurtic is thin tailed. But leptokurtic is more thinner and pointy than platykurtic ...
1
vote
2answers
418 views

Required number of random numbers for using Central Limit Theorem

I wanted to know how many i.i.d random variables have to be summed in order to be able to use Central Limit Theorem. I know it varies depending on the distribution, but does there exist any number $N$,...
1
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1answer
617 views

Regression plot and function for: heavy-tailed probability distribution

I've got data points from a simulation as coordinates in a text-files like so: ...
14
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1answer
2k views

Example of heavy-tailed distribution that is not long-tailed

From readings about heavy-, and long-tailed distributions, I understood that all long-tailed distributions are heavy-tailed, but not all heavy-tailed distributions are long-tailed. Could somebody ...
2
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2answers
514 views

Modeling web traffic distribution

I have to test some functionalities of a software. I need to simulate the web traffic to a server in terms of the numbers of access. What it is the most suitable function distribution for this task?
0
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0answers
638 views

How to characterize opposite of heavy tailed distribution?

I have a bunch of histogram distributions. In some of the histograms (let's call these Type-A), the initial 2-3 bins are extremely tall compared to the remaining bins. In others, there is no ...
2
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0answers
151 views

Exponent value in long tail phenomenon of online store

I've read (pdf) that there is a long-tail phenomenon (or generalized Zipf law) in popularity of retail items: If I sort items for sale by their popularity, I will see a long tail of not very popular ...
1
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1answer
443 views

Extreme Value Theory and heavy (long) tailed distributions

I'm analyzing data about which I have a strong suspicion that it is self-similar (Hurst parameter ranging from 0.60 to 0.78 depending on estimation method and sample sequence). I also observe high ...
2
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1answer
784 views

Is there a binomial regression model that captures data with fat tails?

Specifically, are there any binomial regression models that use a kernel with heavier tails and higher kurtosis than the standard kernels (logistic/probit/cloglog)? As a function of the linear ...
3
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2answers
3k views

How to best plot a heavy vs light tailed distribution in R

I want to create a plot that overlays a heavy vs light tailed distribution as an example and am trying to figure out the best way to do this. I can plot gamma distribution which is light tailed and a ...
0
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1answer
40 views

Weakly informative priors for “r.v. $\mathbf{x}$ is not close to $\mathbf{x}_0$”?

Given some fixed vector $\mathbf{x}_0\in\mathbb{R}^d$, I want to put a prior on a random variable $\mathbf{x}\in\mathbb{R}^d$ so that "it's not very close to $\mathbf{x}_0$". For the moment I put a ...
1
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1answer
349 views

Heavy-tailed distribution with closed-form ML fit from data

Which (if any) heavy-tailed distributions can we compute the maximum likelihood parameters of, given some data to fit the distribution to?
2
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1answer
1k views

Sampling from a long tailed distribution

I have about 500K records from a dataset that consists of counts (so every record is a count of something, like the number of attempts by an IP address to connect to a website). I know, a priori, ...
41
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3answers
14k views

Which has the heavier tail, lognormal or gamma?

(This is based on a question that just came to me via email; I've added some context from a previous brief conversation with the same person.) Last year I was told that the gamma distribution is ...

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