# 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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### Estimating parameters of a Pareto-like distribution and examining its goodness-of-fit

I have developed a theoretical distribution in the form of $$f(x) = \frac{\beta}{\alpha}\left(1+\frac{x}{\alpha}\right)^{-\beta - 1}$$ Where $\alpha$ and $\beta$ are parameters of the model with ...
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### Fit a tapered Pareto distribution in R

Are there any R packages that I can use to fit a tapered Pareto distribution thru Maximum Likelihood? Preferably, I am looking for something that can return the confidence intervals of the parameters ...
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### Pareto distribution with Gamma prior on parameter $\theta$

I want to calculate the posterior distribution of Pareto distribution with known parameter $X_m$ and unknown parameter $\theta$, with conjugate prior on $\theta$ the Gamma distribution: My effort is ...
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### A problem with the expectation of a Pareto

My course notes (3rd-year module in Bayesian Statistics, unpublished) contain the following section. Assume we have data on the number of people queuing at an ATM at a specific hour for several ...
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### Help analysing Mean Residual Life Plot for GPD

I'm trying to fit a GPD for a set of time dependant data. I have two columns, data which is a value on the negative real line where values closest to zero are considered extremes, and time. Using only ...
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### GPD MLE for Multiple Samples

So this is not the exact data I have, but I was more just wondering the approach for this problem. To demonstrate the problem I have, I will give an example. Say we are measuring Wind Speeds in a ...
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### What likelihood to use to model sample means from a Pareto-like distribution?

Suppose there is a random variable with Lomax (Pareto Type II) probability density $$P(x; c) = \frac{c}{(1 + x )^{c + 1}}, \quad x \ge 0, c > 0.$$ Let's draw n_samples=30000 samples of length ...
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### Numerical Solution of two convoluted stable paretian random variables

I am trying to numerically compute the joint density of X and Y, where both are stable paretian distributed random variables with different alphas (1.4 and 1.7). I can compute the PDF via inversion ...
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### Does statistically simple algos qualify as AI algos?

We have a customer purchase transaction history data with variables like below recency - how recently they bought? frequency - How often they bought? monetary - How much value did they bring to the ...
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### Given n iid Pareto distributed random variables, find the UMP one sided test of the first moment

Given $X_1,...,X_n$ ($n\geq 2$) are iid and each have density: $f_X(x) = \frac{c^\theta \theta}{x^{1+\theta}}\mathbb{1}(x> c)$ for known $c$ and $\theta > 1$ then we can easily find the first ...
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### GPD and GEV Fitting: Maximum Likelihood vs. Least Squares

I am trying to build a model based on real world data which involves fitting generalized extreme value distributions and generalized Pareto distributions. Most literature immediately turns to the ...
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### Connection between forms for Generalized Pareto Distribution

On Wikipedia (https://en.wikipedia.org/wiki/Pareto_distribution#Pareto_types_I–IV) one can find the relation between the different types of Pareto Distribution and the Generalized Pareto Distribution (...
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### Existence of Moments for Linear Regression With Pareto Error

Suppose I have the following model linear regression model: $y = \beta_0 + x_1i\beta_1 + x_2i\beta_2 + e_i$ with $e_i \sim Pareto(k,\alpha)$ Now if $1< \alpha < 2$, I would suppose that the ...
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### Confidence Interval Pareto Dist

Let $X_1,...,X_n$ be iid random variables from Pareto distribution with the following distribution $\theta a^{\theta} x^{-(\theta+1)}$, $x>a, \theta >1, a>0$ I have to find a $100(1-a)\%$ CI ...
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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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