# Tagged Questions

The Pareto distribution is a power distribution which was initially invented to describe the distribution of income but has found application in many other areas.

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### Extreme value theory: GPD larger expected value than average

We're using extreme value theory to model tail risks on our portfolio. After we choose the threshold, we fit generalized Pareto distribution to our data over the threshold. The expected value of GPD ...
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### Theoretical/intuitive question about time-varying Generalized Pareto Distribution

I fitted the GPD to the right tail of nine log return series (I multiplied log returns by -1, so modeling the right tail equals modeling the losses) with a threshold equal to the 95% quantile. Some of ...
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### How do you calculate the pareto shape parameter?

I have a set of data that shows a pareto distribution. I am trying to figure out the probability of an event within that data set. I need to know the pareto shape parameter in order to calculate this ...
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### Is the variability index valid for the Pareto distribution

The Pareto distribution is defined from the CDF: $$F^{-1}(p) = \frac{b}{(1 − p)^{1/a}},\ 0 < p < 1,$$ where, $b$ is the scale parameter and $a$ is the shape parameter. In the Gaussian ...
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### Required: Method of moments fitting routine for the two-parameter generalized Pareto

I am currently using the evd package which fits a two-parameter GPD by maximum likelihood. Since in small samples the MOM is superior to the ML estimation I'd like ...
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### Long tail of pareto vs. pearson IV distribution

I am told that wealth follows a Pareto distribution, and that IQ follows a Pearson IV distribution (http://www.abelard.org/burt/burt-ie.asp). Both Pareto and Pearson IV distributions have long tails. ...
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### Does it make sense to fit a Pareto Curve to sales data?

The Pareto principle is used surprisingly widely in business. I'm wondering how correct it's wide use is. It seems as though it is often used without empirical verification as if the situation fits a ...
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### Kullback-Leibler divergence Pareto Distribution

What is the Kullback-Leibler divergence for a Pareto Distribution? Given $p(x)$ = $\alpha$ $\frac{x^{\alpha}_{min,1}}{x^{a+1}}$.
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### How should I interpret these strange density and mixing plots when fitting a generalised pareto distribution using MCMC with JAGS?

I'm trying to fit a generalised pareto distribution to a simulated dataset using JAGS and runjags. When doing so, I get very strange density and mixing plots for the mu parameter. The sigma and xi ...
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### Pearson 5/Inverse Gamma/ Double Pareto

My current research deals with landslide size frequency distribution which has been fit to a three-parameter inverse gamma function and a double Pareto function by previous researchers. I am trained ...
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### How to derive the $\alpha$ for the Pareto rule

Suppose we have the CDF for the Pareto Distribution given by: $$P(X \leq x) = 1-\left(\frac{x_m}{x}\right)^\alpha \;\;\;\;\;\;\;\;\;\; x \geq x_m$$ What is the intuitive way to find the alpha for ...
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### Why is it that it is self-defeating to use the posterior mode as the bayes estimator in this case?

I am reading through an applied statistics book and in it, it makes a very luminous statement for a posterior case where the likelihood was taken from $X_1,...,X_n$ iid random variables from a ...
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### How to get Pareto IV parameter estimates

I have a serie with 850 observations, and I need to fit the Pareto IV distribution. How could I do this in R? I read the guide VGAM, however, I'm not able to run it. If anyone knows, please provide ...
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### Posterior distribution

Suppose $X1,..,X4$ be iid from pdf $f(x|\theta)=\frac{1}{\theta}$ ,for $0<x<\theta$. The prior distribution is $\pi(\theta)=\frac{2}{\theta^3}$ , for $\theta>1$ I have to obtain: a)...
I would like to know if my understanding of the following is correct. This has been tripping me up for a long time now. Compute $\lim_{x\rightarrow \infty}x^{1-\beta}$. This is part of a homework ...