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.

learn more… | top users | synonyms

0
votes
0answers
7 views

Probability of type ii error of Pareto distribution

We are given the Pareto Distribution is of the form FX(x) = 1 − (1 + x)^(-1/theta) Earlier, it has been derived that the sample minimum from a Pareto function is also Pareto distributed, with ...
0
votes
0answers
17 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?
5
votes
0answers
61 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 ...
0
votes
0answers
23 views

How to find yearly return level form hourly data?

I have hourly values from which I extract every data over a threshold (Peak-over-threshold method). I then filter those extreme values so that i only get one value in a given 48 hours period. This ...
1
vote
0answers
46 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 ...
4
votes
3answers
209 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 ...
2
votes
1answer
91 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 ...
2
votes
2answers
56 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 ...
2
votes
1answer
45 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}} & ...
5
votes
1answer
96 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 ...
1
vote
0answers
14 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. ...
4
votes
2answers
74 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 ...
0
votes
0answers
27 views

Which pareto distribution?

How do I assess what Pareto (or similar) function/distribution is most appropriate for fitting my data? I want to be able to model a dataset with a distribution of many-small, few-large that looks ...
0
votes
0answers
36 views

Kullback-Leibler divergence Pareto Distribution

What is the Kullback-Leibler divergence for a Pareto Distribution? Given $p(x)$ = $ \alpha$ $\frac{x^{\alpha}_{min,1}}{x^{a+1}}$.
6
votes
1answer
142 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 ...
1
vote
1answer
73 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 ...
2
votes
1answer
73 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 ...
1
vote
1answer
41 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 ...
1
vote
1answer
99 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 ...
0
votes
0answers
48 views

Recovering values from an estimated Pareto distribution

Recovering values from an estimated Pareto distribution A couple of weeks ago I asked a question about the Pareto distribution, wanting to understand how the units of measurement are related in ...
2
votes
0answers
65 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: ...
2
votes
0answers
51 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 ...
0
votes
1answer
70 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 ...
0
votes
1answer
107 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 ...
2
votes
1answer
146 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 ...
1
vote
1answer
145 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 ...
0
votes
3answers
2k 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 ...
3
votes
2answers
90 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
votes
1answer
158 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 ...
0
votes
0answers
40 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 ...
1
vote
0answers
341 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 ...
1
vote
1answer
774 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 ...
1
vote
0answers
317 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 ...
3
votes
0answers
65 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.
1
vote
1answer
149 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 ...
2
votes
1answer
544 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 ...
4
votes
1answer
826 views

Problem with Pareto distribution and R

I am trying to test this property of pareto distribution: Let f(x) be a pareto distribution $$ f(x)=\alpha \frac{x_m^\alpha}{x^{\alpha+1}} $$ so we have the cdf that is $$ ...
8
votes
1answer
5k views

How do I fit a set of data to a Pareto distribution in R?

Have, let's say, the following data: [1] 8232302 684531 116857 89724 82267 75988 63871 23718 1696 436 439 >[12] 248 235 Want a simple way to fit this (and several ...
0
votes
2answers
188 views

Trouble using pareto levy stable distribution software

I'm using an arcane free program off the internet called "stable.exe" trying to fit a stable distribution curve to a dataset, but I'm having trouble entering the dataset file into the program. When ...
2
votes
0answers
250 views

Understanding the Pareto distribution as applied to wealth

The Pareto distribution can be used to give a pdf for the wealth of a person chosen randomly from a population. (In fact, this was its origin. See, for instance, ...
7
votes
3answers
2k views

How to estimate parameters for Zipf truncated distribution from a data sample?

I have a problem with the estimation parameter for Zipf. My situation is the following: I have a sample set (measured from an experiment that generates calls that should follow a Zipf distribution). ...
14
votes
2answers
4k views

How to calculate Zipf's law coefficient from a set of top frequencies?

I have several query frequencies, and I need to estimate the coefficient of Zipf's law. These are the top frequencies: ...
5
votes
1answer
241 views

How can I apply a Pareto tail to a truncated distribution?

Many income surveys (especially older ones) truncate key variables, such as household income, at some arbitrary point, to protect confidentiality. This point changes over time. This reduces inequality ...