Questions tagged [fat-tails]

Distributions that have greater probability in their tails than would be the case for a normal distribution with the same mean and standard deviation.

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Patton's Symmetric Joe-Clayton copula

I am currently trying to apply Patton's Symmetric Joe-Clayton Copula, described in his "Modelling Asymmetric Exchange Rate Dependence". I am currently looking for the closed-form relation (if there is ...
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1answer
60 views

Kolmogorov Smirnov test vs. Anderson Darling test

I learned that Kolmogorov Smirnov loses sensitivity (power) in the tails, thus it is not adequate for testing goodness-of-fit of fat tailed distributions. However, Anderson Darling test is more ...
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32 views

Non-parametric estimation

This is some sort of an initial question may be I'm asking which may not have a fixed, straightforward answer. But this is very unclear to me. I have come up with some parameter estimation methods for ...
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1answer
43 views

What's the relationship between degrees of freedom of t distribution and tail exponent (alpha) of Pareto distribution?

I'm going to generate a set of data from a T distribution and truncate the body(so that we make it approximately Pareto distributed) of it and estimate the tail exponent(shape parameter) of the ...
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1answer
32 views

What's the formula to estimate the shape parameter of Pareto distribution using weighted least squares method?

I'm trying to simulate my own method using R to estimate the shape parameter of Pareto distributed data by weighted least squares. I searched via several links of research papers, but I could not find ...
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1answer
100 views

When is the posterior distribution equal to the prior?

So I have heard that if the prior distribution is in the subexponential class, applying Bayes rule does not change the belief. I have been trying to find an example of this but I am unable to do so. I ...
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24 views

Comparing two computer generated datasets

I have created an artificial stock market where different groups of traders trade with each other and therefore influence the asset price as well as the returns on the asset. The model generates 10k+ ...
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74 views

How to express tail index as an expectation (for MaxEnt procedure)

I'm trying to construct a prior probability density function, $f_X(x)$, for a fat-tailed distribution using the maximum entropy (MaxEnt) method. For my known "testable" information, I have the ...
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1answer
301 views

Fat Tails and Volatility clustering relationship

Let's say I have a return time series that after a proper ARMA modelling exhibits fat-tallness from QQ-plot. Can this be a consequence of volatility clustering so that by applying a GARCH model I ...
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55 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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0answers
34 views

Is there a robust estimator of the tail mean that is better than the sample tail mean?

Suppose there is a large but finite population with values drawn from some heavily skewed distributional family with finite mean. I am supplied exogenously with the value of the 95th percentile, ...
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2answers
601 views

Looking for a long-tail distribution with mean=1

I would like to generate random numbers $X$'s from a desired distribution whose properties should meet the following requirements: $X \in [0, \infty) $ The mean of the r.v. is around 1, i.e., $\...
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2answers
432 views

A Markov process has a Gaussian stationary distribution. What is implied about the tails of the conditional distribution?

Suppose that for all $t\in\mathbb{Z}$, the distribution of $x_t|x_{t-1},x_{t-2},\dots$ has probability density function $f(x_t|x_{t-1})$, where $x_t,x_{t-1}\in\mathbb{R}^n$. Suppose further that the ...
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1k views

Robust Z-scores for skewed and long-tails distributions

Hope you can help me with my 2 (or 3) questions here below. I want to add/sum some variables having different units. I decide to standardize (Z-scores) the values and then, once transformed in Z-...
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2answers
107 views

Is there a closed-form solution for the tail index of a GB2 distribution?

In the Generalized Beta distribution of the second kind (GB2), where a, p, and q are shape parameters and b is a scale parameter, the pdf is defined on $\mathbb{R}_+$ by: $$ GB2(y;a,b,p,q) = \frac{|a|...
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0answers
22 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 ...
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396 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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1answer
167 views

Heavy-Tailed Data

I'm currently trying to perform a point-biserial correlation on my data, but can't seem to get the continuous data to follow a normal distribution. I've looked into other answers on this website and ...
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1answer
25 views

Identifying candidate distributions with a desired set of qualitative characteristics

Is there a good way of finding candidate distributions based on a set of qualitative characteristics? For instance, at the moment I am looking for a continuous univariate two-parameter distribution, ...
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0answers
60 views

What is a hooked powerlaw?

I happened to encounter lots of scientific/business scenarios where a Zipf/Pareto/powerlaw describes well my data. However, whenever the mean of the distribution is large enough, the fact that these ...
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1answer
53 views

Alternative Copula Tails Meaning

For a bivariate copula $C(u_1,u_2)$, tails are defined as the values $(u,u) \downarrow 0$ and $\uparrow 1$, i.e. the lower left and upper right corners. I would like to know what happens if we go into ...
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1answer
278 views

What is the heaviest tail possible for a continuous normalizable distribution?

The heaviest tailed smooth normalizable continuous distributions that I am familiar with are those with fat power-law tails $\frac{1}{x^{1+\alpha}}$, e.g. a Pareto with $\alpha\rightarrow 0^+$ or a ...
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3answers
684 views

Fat tail? Short tail? Long tail? Where do I go from here?

I am running a linear mixed model with 4 fixed factors and 1 random factor. The response variable is %growth and it has negative values (some of my animals shrunk). The problem I'm having is the ...
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0answers
82 views

Can we improve on the sample mean as an estimator of the true mean of a Pareto distribution, 1 < α < 2?

Suppose I have a sample drawn from a population which is approximately distributed i.i.d. according to the Pareto distribution for values of x greater than X*. Suppose, moreover, that the tail index 1 ...
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199 views

Aggregate variance function and Hurst parameter

What is the aggregate variance method for estimating the value of Hurst exponent? How does it measure long range dependence?
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57 views

Comparing the heaviness of two datasets?

I have two datasets (1 million vs. 500 thousand). The first involves the citation counts of publications indexed by two prominent databases (group 1) (i.e. db1 and db2). The second contains the ...
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74 views

Tail parameter of transformed data

Suppose I have a variable r that has a tail index $\alpha$. How can I know the new tail index if I transform the data, for example using $r^2$ instead? I am using the Hill estimator to estimate the ...
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0answers
2k views

Difference between light tail and heavy tail distribution [duplicate]

I read numerous websites including wikipedia on heavy and light tail distributions. However, I am not quite understanding the distinction between the two. In some sources, it notes that light tail ...
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1answer
299 views

test if two distributions are different based on the tails

First of all, I already read the answer to this question Testing two independent samples for null of same skew?, but I would like to know how to apply it to my data. I have two sets of p-values (...
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1answer
1k views

How is the tail of a distribution defined (about heavy-tailed distributions)?

Some distributions are said to be heavy-tailed. It seems that one definition of a heavy-tailed distribution is that its tails are heavier than the tails of an exponential distribution. However, how ...
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0answers
53 views

Fat-tailed proposal distribution

I am solving a program using my own MCMC Bayesian code. I block propose my vector by calculating the co-variance using the last 10 000 steps (sampling my posterior). I want to implement a fat-tailed ...
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1answer
32 views

Software for computing with extremely wide probability distributions

My friend and I need to make some calculations involving probability distributions over extremely wide ranges of values. For example, I want to be able to take a bunch of random variables with ...
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3answers
682 views

Tail probability for heavy tailed distributions

For some data (where I have the mean and standard deviation) I currently estimate the probability of getting samples greater than some x by using the Q function; i....
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0answers
84 views

What do we know about the rate of convergence of the mean of RVs with infinite variance?

What, if anything, do we know about the rate of convergence of of the mean of identically distributed, independent or stationary random variables drawn from a distribution with a finite mean and ...
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1answer
760 views

When does the law of large numbers hold for RVs from a distribution with infinite variance?

Under what conditions does the law of large numbers hold (or fail, if that is easier to describe) for independent identically distributed random variables drawn from a distribution with a finite mean ...
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0answers
55 views

How can I scale the $k$-th moment of a time series to a different time frequency?

I have a time series, let's say N daily log-returns. I want to study the moments (possibly the distribution) of the weekly returns. I have two ways: 1) Using the time-additivity property of ...
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2answers
583 views

Is the logarithmic transformation sufficient to tame every distribution?

Today I realized a quite known fact. The log transformation of a random variable, drawn from a fat tail distribution, maps into an exponential tail distribution. ...
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3answers
3k views

Central limit theorem and the Pareto distribution

Can somebody please provide a simple (lay person) explanation of the relationship between Pareto distributions and the Central Limit Theorem (e.g. does it apply? Why/ why not?)? I am trying to ...
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2answers
760 views

Is the Student-t distribution a Lévy stable distribution?

Let $X$ have a Student-t distribution, so that \begin{align*} f_X(x|\nu ,\mu ,\beta) = \frac{\Gamma (\frac{\nu+1}{2})}{\Gamma (\frac{\nu}{2}) \sqrt{\pi \nu} \beta} \left(1+\frac{1}{\nu}\left(\frac{x - ...
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40 views

Measuring Autocorrelation in Tail Events

I have a single time series of financial data (stock index returns) and would like to study the autocorrelation among (log-)returns that are classified as "extreme", for example via exceedance of a ...
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0answers
50 views

Nonparametric estimation with Fat Tails in Error Distribution

I'm struggling to understand what a fat tail in the error distribution means intuitively. Therefore I am also not completely sure, why this is relevant for nonparametric estimation. Clearly we are ...
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3answers
5k 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 ...
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2answers
409 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?
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0answers
76 views

Estimation of Distributions with Fat Tails

I work on estimation of income distributions. When I have very high inequality situation I have these two options: Estimate a conventional distribution (e.g. generalize beta) where the parameters go ...
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3answers
3k views

Is a fat tail same as skew

I keep hearing these terms, and it seems like both refer to the same thing: a greater probability of an event occurring at the extreme values of a distribution, far away from the mean (more than 3 ...
2
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1answer
395 views

Models for fat tails

I am trying to model stock returns and I thought it would be interesting to make a comparison between some well-known models. Could anyone name some well-known models that are used in the presence of ...
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0answers
104 views

Fat-tailed data and SVM

Does SVM perform poorly when fat-tailed data with outliers is used? What are some things that could be done to improve learning with such data? Does the choice of kernel and/or kernel parameter ...
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0answers
130 views

Comparing two values in a normal distribution after cutting off the tail of the distribution

I'm doing a sports-related analysis about comparing regular-season performance versus playoff performance, in particular which teams tend to do better during the playoffs. Thus, I'm making a "regular ...
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3answers
8k views

Defining Tail Dependence

I have been trying to find a simple, concise definition of what tail dependence is. Could anybody share what they believe it is. Secondly, if i were to plot simulations using different copulas on a ...
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1answer
545 views

What is the distribution family where one side is with light tail but the other side with heavy tail?

For example the distribution of weights of human. There are not many adults under 40 kg, but a lot more people heavier than 100 kg, although the average of an adult's weight is, let's say, 70 kg. ...