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).

125 questions
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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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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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Why does a minimum value cutoff in edge values create this shape in the log-log plot of the edge values aggregated to start nodes?

I have a weighted network dataset that looks like this: The prev and curr values contain webpages, and n is the number of times users went from the prev webpage to curr webpage. So, each data row is ...
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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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Method for clustering multiple power law variables

Are there any clustering methods suitable for clustering high dimensional datasets that are composed of multiple highly skewed variables, including power law distributed variables? I am considering ...
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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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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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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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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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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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How is a negative binomial regression model different from OLS with a logged outcome variable?

I often deal with distributions of outcome variables that are highly skewed (power-law-like), and I typically want to predict these outcomes. I am wondering when it is appropriate to take a log of ...
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Parametrize fat tailed distributions

I have a empirical distribution with fat tails (i.e. $pdf(x) \sim x^{-\zeta-1}$). I want to reduce the dimensionality of this object: for any integer $k$, I want a $k-$parametric family of ...
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Can I use information about the distribution of the dependent to improve prediction?

I'm trying to make predictions about a quantity on a per-subject basis. If I aggregate my complete sample I can get very good fit for distributions like gamma or Weibull, so I can make some ...
I am studying social network analysis for air travel, and now I am focusing my attention on the power law distribution, $P(k)=ck^{-r}$. I'm trying to estimate $r$ and $c$ with rstudio. [...