# Questions tagged [pareto-distribution]

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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### How do I fit a distribution using fitdist if I already know the parameters? [closed]

I am fitting a Pareto distribution to some data and have already estimated the maximum likelihood estimates for the data. Now I need to create a fitdist object from it, but I am not sure how to do ...
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### Fitting a lognormal-pareto distribution to empirical data distribution in R

Let's say I have data whose distribution is leptokurtic, with a lognormal peak and a pareto tail (for this question, I will generate lognormal-pareto data using package CompLognormal but I will need ...
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### How to implement a GLM with Pareto family?

My data fits a Pareto Distribution very well, better than normal exponential, gamma, lognormal, etc. I am trying to find a way to implement a GLM with a Pareto family flag. Ideally I can then run ...
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### Discerning differences in groups with millions of datapoints: is a GLM even valid?

I have a MASSIVE dataset of 22 million shrubs from a basin in the southwest US. I have selected 2 response variables which are both positive continuous variables: Shrub Canopy Volume (cubic meters) &...
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### Measuring Pareto like metrics for series or dataset [closed]

Pareto rule states that 20% of records accounts for 80% of total. Actually it's just a special case for a certain dataset. If we use a series: from 1 to 10 we can easily see that Pareto rule ...
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### Fitting a mixture model distribution to kurtotic data

I need to fit a parametric distribution to data that has non-zero (unknown) kurtosis. First I tried to fit a Pearson type VII / Student's t, but the fitting is especially poor in the two tails, ...
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### Building a mixture model that fits well to the tail of a kurtotic distribution

I need to fit a distribution to data that has non-zero (unknown) kurtosis. I tried to fit a Pearson type VII / Student's t, but the fitting is especially poor in the two tails, possibly due to less ...
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### Fitted value for Generealized Pareto Distribution Regression

Let say I want to build a model of regression Pareto for the value extreme in payment of damage for insurance. The code in R: ...
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### Compare return levels of fitted GPD using MLE in different R packages

This question is related to this post: Different quantiles of a fitted GPD in different R packages? I want to constraint "potvalues" data to be in a period of 6 years, this is, 16 observations per ...
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### Error while fitting Pareto type 2 distribution

I am trying to fit a pareto type 2 distribution using the following code: ...
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### Validity of Monte-Carlo method to estimate a probability distribution which follows a power law

I am using a Monte-Carlo method to estimate a probability distribution function (pdf). Basically, I have several input parameters following known distributions, from which I can draw samples, that I ...
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### 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 ...
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### Robust sum of non-independent random variables

What approach could be used to sum non-independent variables? I have probability distributions of stock prices and want to calculate the probability distribution of the portfolio price (sum of some ...
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### How can I calculate the exponent (parameter or tail index) of the Pareto distribution associated to the following paperclips experiment?

The experiment is the following: take a pool of paperclips for which in each round we follow these steps: 1) choose two paperclips randomly 2) if they are not linked with each other then link them ...
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### Processes that converge to the Pareto distribution

Do any stochastic processes generate the Pareto distribution as the steady-state statistic of the ensemble? For example, $$dS_t = f(t, S_t, W_t)$$ where in the Ito sense the p.d.f. of $g(S_t)$ ...
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### If $X\sim \operatorname{lognormal}$ then $Y:=(X-d\mid x\geq d)$ has approximately a Generalized Pareto distribution

Let $X$ be a random variable with lognormal distribution. Show that when sufficiently large then $Y:=(X-d\mid x\geq d)$ is approximately a random variable with generalized Pareto distribution. Hint: ...
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### How does the Pareto principle give the 80/20 rule?

It seems to me that the Pareto principle says that for any $n$-many people that produced $m$-many goods, $\sqrt{n}$-many people would produce $\frac{m}{2}$ many goods out of the total $m$ many ...
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### Are there any non parametric tests to check for Pareto data?

I'm in search of a non parametric test to check whether my data are Pareto distributed, but I couldn't find a proper reference for it. I'm using R to simulate these so if there's any R in built test, ...
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### How can Pareto(alpha = 5, x_min = 2) be heavy-tailed where alpha is the shape parameter or the tail index?

Point 1 : It's known that, usually, when the tail-index (alpha) is between 0 and 2, of a certain data set, the distribution is considered as heavy-tailed. Point 2 : It's know that Pareto ...
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### What's the relationship between Pareto shape parameter (alpha) and exponential rate parameter (lambda)?

I'm trying to do my undergraduate research on non parametric density estimation for a heavy tailed distribution. For that, I'm with a data set, which I assumed it should be Pareto distributed with ...
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