Questions tagged [power-law]

A power-law is a function that increases proportionally to a power of its argument (ax^b). Often seen in fitted relationships or in densities (power-law distributions).

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35 views

Why do poweRlaw and fitdistrplus differ in fitted lognorm parameters

I am trying to evaluate whether a power-law fit is appropriate for some data of lake areas that we have, and whether the theoretically supported alternative of the log-normal, at least at the tails, ...
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Appropriate Data Analysis when Criterion has Heavy-Tailed Distribution

I have a data set where my independent variables (i.e., personality assessment scores) are continuous and follow a normal distribution. The criterion, sales performance, is heavy-tailed and follows a ...
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How to interpret kernel coefficients in Hawkes Models

I am learning Hawkes Models application in Finance. I was reading the following article, which uses Tick for Python to estimate kernels as a power law. I could not understand what those values in ...
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29 views

Why Are Bell Curves Used for Performance Appraisals?

Why do organizations that stack-rank employees force-fit employee rankings to a bell curve? Is there any theoretical or emperical evidence to support a normal or near-normal distribution of ...
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135 views

Cut off long tail of distribution (no matter how long is the tail) [closed]

One of the algorithms that we are working on is designed to report the time it takes for people to finish the onboarding process in an app. We need an algorithm to eliminate the long tail of a ...
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23 views

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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How to perform the Kolmogorov-Smirnov test on the truncated power-law distributed data?

Recently, I read papers that perform power-law fitting on their empirical data (estimate the alpha), some of them report corresponding p-value for the Kolmogorov-Smirnov test, but many of them do not. ...
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Powerlaw Distribution and old nodes [closed]

I am working on the size of discussions (number of replies, replies to the replies) on Twitter data, and I am observing Power-law distribution for small and medium-size discussion but it is not valid ...
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Rank-size log-log plot inflection: drooping tail of power law

Most of my data seems nicely to fit a power law but with a "drooping tail", which I believe is quite common, although in this case the drop-off is quite steep. I have two related questions if I may ...
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How to Select the Largest Y Values for {X,Y} Pairs, for a Pareto-Distributed Dataset, for a Meaningful Fit?

First, apologies for the inelegant question. Second, on to the question: Background Information: I study impact craters, and the size-frequency distribution (number vs diameter) of impact craters ...
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Statistical significance of power-spectrum estimation

I have a process which resembles red noise and I am trying to assess the validity of some observed peaks in my power-spctral density estimation (i am using welch's method). I have seen in a few papers ...
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32 views

Random Samples from Spliced Distribution

I am studying Clauset, Shalizi, and Newman, Power Law Distributions in Empirical Data (preprint available here) in R. Packages used: ...
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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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Finding the exponents of a multiple power law: is linear regression valid?

I want to fit a multiple power law equation of the form $y = {x_1}^{\alpha_1} {x_2}^{\alpha_2}$ where I have many examples of $y, x_1, x_2$. (Note there is no intercept.) Is it possible for me to ...
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1answer
227 views

Discrete Pareto Distribution vs Zipf Distribution and Power Law vs Zipf Law

I need to get a simple, but clear idea of Discrete Pareto Distribution vs Zipf Distribution and Power Law vs Zipf Law. (Are they similar/ how they relate to each other.) Wikipedia definitions do not ...
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How are these two power law fitting glm models different?

I have some data that I thought I'd try fitting with a power law (in R). ...
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1answer
332 views

Using log-log graph to find equation of power law relationship?

I have a set of data that I think forms a power law relationship, however I am struggling to work out the equation of the relationship. Here is a subset of the data I am working with: ...
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Sum of powers of standard normal random variables

Context: While trying to teach the Central Limit Theorem I thought it would be a good idea to show a case where it breaks down. Question: Consider the sum of increasing powers of standard normal ...
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How well is a power law distribution described by the first four moments?

For a normal distribution, the first two moments (mean and variance) are sufficient statistics for the entire distribution. Suppose I have a power law distribution, and I have data on the first, ...
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267 views

Is the truncated power law a heavy-tailed distribution?

A heavy-tailed distribution is often defined as a distribution with a tail that is not exponentially bounded. A truncated power law (or power law with exponential cut-off) is a distribution that ...
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354 views

Most accurate way to express the income of the top 1% in a power distribution?

I have an array of 50,972 household incomes for a small metro area, and I want to measure how much the so-called top "one-percent" make (e.g., the 99th percentile). As you'd expect, it's a power curve:...
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263 views

Is KS test really appropriate when validating a power law/estimating power law parameters?

I'm attempting to find out whether some highly skewed data are drawn from a power law distribution, following the popular paper by Clauset, Shalizi and Newman, 2009. Clauset et al. use the Kolmogorov-...
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Connection between logit model and power law distribution

I am wondering whether it is appropriate to make a connection between the use of a logit model and a power law distribution. My dependent variable is categorical and ordinal, therefore I am fitting a ...
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1answer
484 views

Calculate Zipf-Mandelbrot parameters from distribution

I am fetching trending topics from social media where the frequency of likes is said to follow a Zipf-Mandelbrot distribution; i.e., some of the posts will have a high number of likes and some other ...
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Determining the number of observations within the tail of a given distribution

I am wondering how to determine the number of observations that fall within the tail of a distribution. I am reading a paper and the authors use the assumption that 50 observations need to fall into ...
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Characterizing/Fitting Word Count Data into Zipf / Power Law / LogNormal

Using NLTK and Pandas, I was able to process some text files and generate word count data for them, and finally create a histogram describing word frequency. However, I'm wondering what kind of ...
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Extracting power of a power law from data

My question is more about the methodology. Assuming in some experiment we have measured quantity $y$ per each unit of time $x.$ So $y$ and $x$ form our data set here. Moreover, we know that they are ...
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“Law of large numbers” for distribution with infinite variance?

This is a purely explorative question. I asked a question here about a "central limit theorem" for random variables with infinite variance. I did not expect it, but it turns out that even some ...
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1answer
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A random variable $X$ on $(0,\infty)$ which behaves like Exp for small $x$ and Pareto for large $x$

Are there any examples of distributions which behave like Exponential for small values and like Pareto for large values. $$\ln \mathbb{P}[X>x] \sim -\lambda x, \qquad \text{ for } x \text{ small}, ...
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101 views

Mixture of power-law distribution

I have two large sets A and B of (integer) numbers, both obtained with two different (and unknown) probability distributions $\rho_A$ and $\rho_B$. A (also large) set C contains a proportion $p$ of ...
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1answer
930 views

Normalization of power-law distributed variables. Z-scores or Min-Max?

I need to make a composite index from the sum of three power-law distributed variables, which vary on different scales and have different variances. For each variable there are many observations with ...
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468 views

Generate random numbers from a power-law/exponential distribution

I'm working through the paper Power-law distributions in empirical data by Clauset, Newman and Shalizi. On page 12, they generate random numbers from the following distribution: \begin{equation*} p(...
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Generating random samples from a power law and testing them with R igraph

I haven't looked into power laws before, so the question may very well have an obvious, embarrassing answer. In some ways it dovetails with this post. The problem may be in the method, or in the ...
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What is a hooked powerlaw?

I happened to encounter lots of scientific/business scenarios where a Zipf/Pareto/powerlaw describes well my data. However, whenever the mean of the distribution is large enough, the fact that these ...
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1answer
525 views

Fitting a Pareto distribution to two dimensional data in R

I've looked here: How do I fit a set of data to a Pareto distribution in R? do-i-fit-a-set-of-data-to-a-pareto-distribution-in-r and I've checked out the poweRlaw library which is built for fitting ...
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821 views

Exponential vs Power Regression - which one is more appropriate when data points are limited?

When researching the reciprocity failure (a feature of film photography, otherwise more appropriate to https://photo.stackexchange.com/) I have run into a statistical issue. I have a datasheet for a ...
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1answer
2k views

Estimate power law exponent for node degree distribution in scale free networks

I am trying to use the powerlaw python package to estimate the power law exponent of the degree distribution in a graph. As a reference I am using ...
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612 views

Input to fit a power-law to degree distribution of a network

I would like to use R to test whether the degree distribution of a network behave like a power-law with scale-free property. Nonetheless, I've read diferent people ...
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1answer
472 views

Log-likelihood in fit_power_law{igraph}

The R package igraph has the fit_power_law function which, as you can imagine, can fit a ...
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2k views

Fitting a power law to the relationship between two variables

I have a small set of data that I need to fit a curve to (see image and data below). ...
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134 views

How to adjust your dataset so it fits a power-law? [closed]

I have created a dataset of pictures taken at the museum of different paintings. The dataset is divided into 113 different categories (paintings) and contains around 4.8k images. Just to be clear: ...
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639 views

Does my data follow power law distribution? dummy approach in R

I am trying to test if my data fits the inverse power law distribution. Specifically, I am interested if my damaged area (Shape_Area) is somehow distance dependent? I tried to apply examples from ...
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167 views

Zero-inflated + thick-tailed + unbalanced panel

I'm pretty new to statistics and need advice on how to analyse zero-inflated, thick-tailed, panel distributions. My sample is a count of enterprise births per city and per year across U.S. cities and ...
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1answer
224 views

what can I infer if my data follows power law?

I am working on data set of "Number of days taken to get a reply to mail". I have studied POWER-LAW DISTRIBUTIONS IN EMPIRICAL DATA - AARON CLAUSET. I have used powerLaw package in R to find if my ...
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Evaluating the improvement in goodness-of-fit (power function fits)

Imagine an experiment where 15 participants are presented with pictures. Each picture is presented 8 times (within-subject design). We want to evaluate the effect of picture repetition (independent ...
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Understanding power laws and log plots (Newman paper)

I'm trying to understand some of the plots in the paper Power laws, Pareto distributions and Zipf’s law by Newman. Here is the figure in question: In this paper he generates synthetic data that ...
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147 views

Linear mixed effect model for Taylor's power law: Random effects variance equal to 0

My project involves stink bug sampling on soybeans and I'm using Taylor's Power law (logvar ~ logmean) to use its parameters in the development of a sampling plan. ...
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314 views

R - power/exponential regression issue

I have the following data which I am trying to get a nice simple regression fit to it: Looks simple enough, but using R's nls function and trying both a power (ax^b+c) and an exponential (ab^x) fits ...
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394 views

Power law is Nested in Power Law with Cutoff?

I'm reading "Power-Law Distributions in Empirical Data": https://arxiv.org/pdf/0706.1062.pdf. The authors make the claim that "In some cases the distributions we wish to compare may be nested, ...
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Why is the slope not back transformed in a regression equation for allometric relationships

I'm learning about allometric relationships and how to derive the parameters from regression equations. I've seen that you can fit a linear regression model by taking the log of both the X and Y ...