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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Is there a distribution that covers Pareto's law?

Is there a distribution where (for example) 80% of the results come from 20% of the inputs? (i.e. Pareto's law). Hmm... there's a tag for Pareto Distribution ... is that the answer?
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247 views

Central limit theorem and the Pareto distribution

Can somebody please provide a simple (lay person) explanation of the relationship between Pareto distributions and the Central Limit Theorem (e.g. does it apply? Why/ why not?)? I am trying to ...
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9 views

Buy Till You Die(BTYD) - Individual LTV scores

I'm using the Buy Till You Die(BTYD) package in R to predict LTV (using Pareto/NBD), and I've been able to produced expected transactions by week, but is there a way to predict the dollar value of ...
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29 views

Bias of method of moments estimator for Pareto distribution with known scale parameter

Let $x$ be a Pareto distribution with a known scale parameter $m>0$, i.e. $x\sim f(x|a)=\frac{am^a}{x^{a+1}}, x>a, a>0$ $\mathrm{E}\left[X\right]=\frac{am}{a-1}$ Using method of moments ...
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47 views

How should I solve the following simultaneous equations?

I have the set of simultaneous equations below from the paper Parameter estimation for 3-parameter generalized pareto distribution by the principle of maximum entropy (POME) by VP Singh and H Guo: $$ ...
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45 views

How do I use NLOpt (C++) to solve for Generalized Pareto Distribution Parameters?

For some research I need to find the parameters of the Generalized Pareto Distribution. I plan to do this by minimizing the following function: $$ -\sum_{i=1}^{n_u} ln((1/\sigma)(1+\xi((x_i - ...
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17 views

Invalid returned matrix for Density function in Pareto Survival Analysis

I want to perform a survival analysis using survreg procedure from survival library in R for a pareto distribution (I based my ...
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1answer
96 views

Have MLE estimators for Generalized Pareto Distribution. Given a known value of $c$, how do I calculate $a$ and $b$ using the provided estimators?

I am doing research into the three parameter Generalized Pareto Distribution $$ f(x|a,b,c) = \frac 1 b\left(1+a\left(\frac{x-c}{b}\right)\right)^{\big(-1-\frac 1 a\big)} $$ for finding VaR and CVaR. ...
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39 views

Posterior of alpha parameter (Shape) of Pareto Distribution

Im trying to generate the posterior distribution of $\alpha$ parameter of Pareto Distribution. I did all the job correctly on paper, but when i go to implement in R i have some problems.I have a ...
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81 views

R- get qq plot for Pareto distribution

I'd like to use R to do a qq plot on my data for a Pareto distribution. I've been able to do this for the lognormal (my code is below) but fitdistr() doesn't support the Pareto. I've tried a similar ...
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12 views

Fitting a power law to existing integral

I have empirical data - people from cities - a certain number of people for a certain number of cities. I know the exact number of cities, as well as the exact number of total people - e.g. the ...
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206 views

How to fit a function to a CDF in R?

I've been given a dataframe that contains data for a CDF. The column X contains the 250 $X$ values, and the column P contains ...
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1answer
284 views

Cramer Von Mises - How to use this test correctly?

I had a problem when I tried to test the fitting of my data with the generalized Pareto distribution. I used the MLE to estimate the two parameters 'shape' and 'scale' and I generated a vector of ...
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70 views

Pareto 2 distribution

I am bit confused between Pareto and Pareto Type II distribution. In the actuar library (page 64), details of pareto distribution are given. However, in the end, it is mentioned that "Distribution ...
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1answer
83 views

Weighting observations and measurement uncertainty in bayes

I am working on using MCMC (via STAN) to estimate model parameters for a bunch of observations with measurement uncertainty. I'm having problems with weighting each observation, and have reduced the ...
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149 views

Hyperprior Noninformative Beta Binomial Model

I've been working through Gelman's Bayesian Data Analysis 3 text and have been trying to understand one of the hierarchical models revolving around rat tumors (Chapter 5). He uses a binomial model ...
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55 views

What is the name of this distribution family?

I am trying to identify this probability density function so I can read up on it to find confidence intervals for $\theta$: $$f(x;\theta,v)=\frac{\theta v^\theta}{x^{\theta+1}}I_{[v,\infty)]}(x);\ ...
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30 views

Does the generalized beta distribution of McDonald and Xu constitute an exponential family?

Does the generalized beta distribution of McDonald and Xu, J. Econometrics 66 (1995) 133-152, constitute an exponential family? Can it be written in a way that makes this more obvious? Alternatively, ...
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303 views

Pareto two-tailed GLM regression

How can I perform a Pareto two-tailed GLM regression? Any reference to link functions and code in R?
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120 views

What distribution results in adding two Pareto distributions

I'm wondering what distribution results in adding two (or more) type-one Pareto distributions of the form $x^{-\alpha}$. Experimentally, it looks like a two-mode power-law, asymptotic to the ...
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94 views

Evaluate goodness-of-fit of estimation of Pareto-like distribution

I would like to evaluate the goodness-of-fit of the following (Pareto-like) distribution: $$ f(r) = \sigma \centerdot r^{-\rho} $$ The function estimates the population of cities given the rank $r$ in ...
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3answers
259 views

In a “bursty” dataset, how do you filter for the few important values that make up the bulk of the information?

Note sure if there is an existing stats concept for this but I have a dataset that consists of mostly small data points with a few large ones. e.g. 1 2 1 3 1 2 87 3 2 1 1 1 1 3 1 2 1 1 1 99 How can ...
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1answer
204 views

Kolmogorov-Smirnov for Pareto distribution on sample

I want to use the Kolmogorov-Smirnov test to test if a sample is drawn from a Pareto distribution. Unfortunately, the only way to estimate the distribution's parameters is from the sample. Does ...
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2answers
148 views

Is there a package for three parameter inverse gaussian or lognormal distributions in C++?

I want to generate random numbers from one of the following distribution in C++. I haven't been able to find any libraries though. Do they exist? In order of preference: Three parameter inverse ...
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487 views

Moments of the two-parameter generalized Pareto distribution (GPD) needed

In this thread the first two moments of the two-parameter GPD are given, where the distribution might be defined as $G(y)= \begin{cases} 1-\left(1+ \frac{\xi y}{\beta} \right)^{-\frac{1}{\xi}} & ...
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287 views

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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42 views

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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217 views

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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71 views

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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252 views

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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148 views

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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1answer
115 views

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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56 views

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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1answer
227 views

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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83 views

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: ...
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70 views

Is it appropriate to estimate a Pareto regression's α by maximising R-squared?

Fitting a power law regression. What are the downsides of estimating α by maximising the R-squared of (a) the theoretical values output by the regression with the candidate α and (b) the empirical ...
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1answer
103 views

Expectation of the Pareto distribution [closed]

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 ...
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1answer
255 views

Why am I getting this result in modeling a Pareto Type II distribution in Excel?

In Excel for a project I'm trying to model the density, distribution and survival function ($1-F(X)$) and I can't get the density to sum to one and I can't get the distribution to go to one. For the ...
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1answer
298 views

Can the mean deviation about mean exceed the standard deviation for the Pareto distribution?

Can the mean deviation about mean exceed the standard deviation for the Pareto distribution? I just went through some books and found they are claiming that it cannot. How can I prove that? What is ...
2
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1answer
217 views

How to use the Pareto distribution in fitting survival curves?

I have a series of numbers, which are some survival probabilities that form a decaying curve. I would like to fit them with a "Pareto" distribution. I expect to have a smooth fitted curve, thus I can ...
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3answers
3k views

Fitting data in a generalized Pareto distribution and parameter estimation

I have log(return) data as time series, how I can fit this data in a Generalized Pareto distribution and estimate the parameters of this distribution, any kind of resource pointer with clear code ...
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2answers
155 views

Probability of period without event

I have a data set of a list of invoices each of which have a date. I'm trying to detect when I might consider that a customer has stopped ordering a part. The way I'm approaching this might be ...
4
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1answer
269 views

Can an estimator of the mean of a distribution with no variance have a variance?

Suppose you have a sample from a distribution with a mean but no defined variance, like the Pareto with tail parameter between 1 and 2, or Student’s t with 2 degrees of freedom. Can an unbiased ...
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50 views

Gertensgabe and Werner plot

I was told about the Gertensgabe and Werner plot to assess the optimal threshold for a GPD model. However, I did not found neither any R package nor code to implement this. Does anybody have some ...
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599 views

Hypothesis testing for Pareto distributions

I wish to to some simple hypothesis testing of the form provided by T-Tests and ANOVA. However, my data is not normally distributed (it follows a Pareto distribution). My understanding is that ...
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1answer
1k views

Selecting threshold for generalized Pareto distribution in R

I'm using the POT Package in R for fitting a Generalized Pareto distribution to my data. For choosing an approximate threshold I'm using the ...
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1answer
489 views

Truncated Pareto estimation

Given min and max values, how can I estimate shape parameter (tail index) of data generated by truncated pareto distribution ? I see a package tpareto but find no information on how to estimate tail ...
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80 views

Lomax distributions - Kullback Leibler divergence

Does anyone know of a reference for an expression for the Kullback-Leibler divergence between two Lomax (Pareto II) distributions? Not really worried which way the Lomax is parameterized.
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185 views

Why does the $\alpha$ parameter grow to $\infty$ in Pareto-distributed random numbers when changing the threshold?

I noted a strange fact. Let X be a set of Pareto distributed random number with $\alpha$ and $x_{min}$ defined a priori. Now, let $\alpha'$ be the estimated value of the shape and $x_{min}'$ be a new ...
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1answer
770 views

Comparing Pareto fitting methods

I am comparing different method of fitting Pareto distributed random numbers. What seems very strange to me is that fitting a straight line in log-log scale has to be the worst numerical method and ...