# Questions tagged [heavy-tailed]

Heavy-tailed distributions have tails that are not exponentially bounded (eg, log-normal & Pareto [heavy right tail], & t [both]). For general questions about fat tails, use the [kurtosis] tag.

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### fitting GAM to longitudinal heavy-tailed count data

I am trying to fit a generalized additive model to the sum of events occurring over a fixed interval (count data >= 1). I would like to model these data as a function of day-of-year and include ...
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### Quantile regression for a sample of city sizes

I would like to estimate the following regression: $$\ln(Rank) = \alpha + \beta \ln(Population)$$ For an ordered sample of city sizes (from biggest to smallest), where $Rank$ is 1 for the biggest 2 ...
65 views

### A follow-up to 'The meaning of an analyt. result concerning the… mean of the square of a reciprocal of a norm. distrib. rand. variable'

This question concerns the same subject matter as this previous question of mine. However, a moderator felt that the questions I posed there are significantly different from the question I am about ...
63 views

### The meaning of an analytical result concerning the (formally nonexistent) mean of the square of a reciprocal of a normally distributed random variable

This question arose as I was writing this answer to this question. Let $X$ be normally distributed with mean $\mu$ and standard deviation $\sigma$, and let $Y=1/X$. First, note that the integral ...
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### How do I interpret parameters from a generalized Pareto distribution?

I fit a generalized Pareto distribution using the function "fitdistcens" from the package "fitdistrplus": ...
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### Quantifying dependence of Cauchy random variables

Given two Cauchy random variables $\theta_1 \sim \mathrm{Cauchy}(x_0^{(1)}, \gamma^{(1)})$ and $\theta_2 \sim \mathrm{Cauchy}(x_0^{(2)}, \gamma^{(2)})$. That are not independent. The dependence ...
149 views

### What does it mean to say that $X_1, X_2$ have a "common" Normal distribution?

An exercise question asks Let $X_1, X_2$ be rvs having a common Normal distribution $N(0,1)$ with $\operatorname{Corr}(X_1, X_2) = \rho$. Calculate the coefficient of upper tail-dependence for all \$...
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### need explanation about the exponent parameter s in zipf distribution

I need to model the popularity of some requested files from a library with Zipf distribution and I want to simulate it in MATLAB. I don't know what's the effect of parameter s on my result. for ...
117 views

### How can I derive the function curve from a histogram of observed data

I'm analysing some datasets that produce heavy tailed data when plotted as a histogram. My initial goal was to attempt to fit a known distribution to my dataset. Thereafter I use to the properties of ...
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### Formal definition of the qqline used in a Q-Q plot

I'm doing some distribution fitting work and I'm looking at Q-Q plots and how they can be used visually to interpret goodness of fit. My data is heavy-tailed so I am looking at Weibull, log-normal, ...
380 views

### Is the truncated power law a heavy-tailed distribution?

A heavy-tailed distribution is often defined as a distribution with a tail that is not exponentially bounded. A truncated power law (or power law with exponential cut-off) is a distribution that ...
551 views

### Choosing bins for chi-square testing distributional fits for distribution similar to normal/heavy-tailed

Chi-squared test can be used to check the hypothesis, that given sample is from the given theoretical distribution. If the distribution is continuous then we should properly choose bins. Question 1 : ...