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 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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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 ...
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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: ...
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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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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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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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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 ...
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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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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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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 ...
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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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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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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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550 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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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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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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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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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 ...
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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 $$ ...
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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 ...
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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 ...
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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, ...
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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). ...
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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: ...
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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 ...