Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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.

72 questions
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Differences between heavy tail and fat tail distributions

I thought heavy tail = fat tail, but some articles I read gave me a sense that they aren't. One of them says: heavy tail means the distribution have infinite jth moment for some integer j. Additionally all the dfs in the pot-domain of attraction of…
Melon
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Comparison of the tails of two sample distributions

I have two set of data that are roughly centered around zero but I suspect that they have different tails. I know a few tests to compare the distribution to a normal distribution, but I would like to compare directly the two distributions. Is there…
RockScience
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Test which distribution has a "longer tail"

I have measured two non-negative random variables, A and B. Their true underlying probabilities are unknown, however, it may be assumed that the probabilities are largest at zero and monotonically decrease for larger values. Most certainly, those…
Aleksejs Fomins
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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 understand the following statement: "the Central Limit…
user1222447
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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 - \mu}{\beta}\right)^2…
Puzzle
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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 graph, how would I know which ones exhibit tail…
Jim
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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 standard deviations away)
Victor
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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. My question is very simple: Is the logarithm sufficient to tame every distribution? I…
emanuele
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Issues with fitting distribution to heavy-tailed data

I am currently trying to fit distributions to some heavy tailed data-set (see the data set below) and have a hard time producing good results: v1 <-…
user3777456
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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 sensitive at the tail, thus is better than KS test for…
Master Shi
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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 does one exactly define the tails, since the…
user133187
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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 so I think leptokurtic is thin tailed... But it…
LKM
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Consistent, non-parametric, robust (to fat tails) estimation of expected value of an asymmetric distribution

Question: Is anyone aware of a consistent, non-parametric estimator of the expected value of an asymmetric distribution that is robust to fat tails? What if we constrain ourselves to the class of continuous (on the real number line) uni-modal…
Colin T Bowers
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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 unconditional (stationary) distribution of $x_t$…
cfp
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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 residuals are not normally distributed according to…
Nathan Haag
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