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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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34 views

Better measure of tail extremity than kurtosis

According to Wikipedia, the only correct interpretation of kurtosis is "tail extremity," the logic being that datapoints within one standard deviation of the mean are raised to the fourth power and ...
89 views

Monte Carlo simulation for the log-normal distribution

Consider $X$ that follows a log-normal distribution with parameters $\mu=1$ and $\sigma=1$. The moments are known: $m_n=E[X^n]=e^{n+n^2/2}$. For example, $m_{10}=e^{60}$ (of the order of $10^{26}$). I ...
139 views

Discrepancies with Actual vs Expected Probabilities for Distribution?

I am attempting to estimate consecutive days worth of sales of specific items in each store: For most stores, the probability (n=1 k=1, n=2 k=2, etc…) that an item will continue to sell over a period ...
10 views

Comparing empirical and theoretical estimates of the number of right-censored values

Suppose I have right-censored data, so that observations are still present but are top-coded. In my case this is income data for, let’s say, individual people, and associated & probability weights....
53 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 ...
25 views

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 ...
150 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 ...
62 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 ...
38 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 ...
125 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 ...
26 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+ ...
77 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 ...
350 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 ...
61 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 ...
35 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, ...
709 views

43 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 ...
51 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 ...
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 ...
447 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?
79 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 ...