# 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.

73 questions
Filter by
Sorted by
Tagged with
247 views

### 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 ...
50 views

### Why Pareto distribution has pointy head? How its symmetrical version looks like?

I want to use Pareto distribution for the stock price probability distribution. They say (B. Mandelbrot and N. Taleb Mild vs Wild Randomness) it represents the price changes, especially the tail ...
38 views

### What is the connection between fat tailedness of student t distribution and sparsity inducement in lower dimensions in context of t-sne

I have read that the t distribution is a heavy tailed distribution in comparison to Normal distribution. Also some say that heavy tailed distributions help in creating more sparsity. My question is ...
47 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 ...
328 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 ...
145 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 ...
15 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....
80 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 ...
26 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 ...
278 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 ...
77 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 ...
45 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 ...
174 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 ...
27 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+ ...
78 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 ...
460 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 ...
75 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, ...
820 views

47 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 ...