Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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).

A power-law is a function that increases proportionally to a power of its argument (ax^b).

Often seen in fitted relationships or in some forms of densities (power-law distributions).

Power-law relationships are common in physics, though non-power-law relationships may also look somewhat like power-laws.

Power laws are also associated with economics, the Pareto principle and the 80-20 rule.

Reference: Wikipedia - Power law

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Interpreting the difference between lognormal and power law distribution (network degree distribution)

First off, I'm not a statistician. However, I have been doing statistical network analysis for my PhD. As part of the network analysis, I plotted a Complementary Cumulative Distribution Function (CCDF) of network degrees. What I found was that,…
Mike
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How to measure/argue the goodness of fit of a trendline to a power law?

I have some data to which I am trying to fit a trendline. I believe the data to follow a power law, and so have plotted the data on log-log axes looking for a straight line. This has resulted in an (almost) straight line and so in Excel I have…
Bryce Thomas
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How to test whether a distribution follows a power law?

I have data on how many users post how many questions. For example, [UserCount, QuestionCount] [2, 100] [9, 10] [3, 80] ... ... This means that 2 users each posted 100 questions, 9 users each posted 10 questions, and so on. So, how can I…
tThirday
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Intuition behind power law distribution

I know that the pdf of a power law distribution is $$ p(x) = \frac{\alpha-1}{x_{\text{min}}} \left(\frac{x}{x_{\text{min}}} \right)^{-\alpha}$$ But what does it intuitively mean if, for example, stock prices follow a power law distribution? Does…
Thomas James
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Do unique visitors to a website follow a power law?

Suppose I have an ordered vector where the first element is the number of visits to a website in a given period of time by the unique IP with the highest number of visits, the second element is the number of visits by the unique IP with the second…
Jon Smark
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Getting the right starting values for an nls model in R

I'm trying to fit a simple power law model to a data set that is as follows: mydf: rev weeks 17906.4 1 5303.72 2 2700.58 3 1696.77 4 947.53 5 362.03 6 The goal being to pass the power line through and use it to predict rev vlaues for future…
NeonBlueHair
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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 difference of alphas.
AMG
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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-Smirnov (KS) statistic to measure the…
JaydenM-C
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Can I do a t-test Power Analysis for Unequal Size Groups which Produces 2 Different Minimum n's?

It's usually straightforward to do a Power Analysis to compute the minimum sample size, especially in R which is my preferred statistical computing environment. However, I am being asked to conduct a Power Analysis that's a little different than…
Hack-R
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Accurately generating variates from discrete power law distribution

What are the best methods to accurately generate random integers distributed according to a power law? The probability of getting $k$ ($k=1,2,\ldots$) should be equal to $p_k = k^{-\gamma} / \zeta(\gamma)$ and the method should work well for any…
Szabolcs
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Definition of heavy-tailed distribution

I'm reading about heavy-tailed distributions, the definition states that: The distribution of a real-valued random variable $X$ is said to have a heavy right tail if the probabilities $\mathbb{P}(X > x)$ decay more slowly than those of any…
Blg Khalil
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Regression for power law

This is a cross post from Math SE. I have some data (running time of an algorithm) and I think it follows a power law $$y_\mathrm{reg} = k x^a$$ I want to determine $k$ and $a$. What I have done so far is to do a linear regression (least squares)…
0x539
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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 the outcome variable and apply OLS, and when it is…
Jeremy
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Fitting a line to a log-log plot

I have some data that I'm playing around with; for simplicity, let's suppose the data contains information on number of posts a blogger has written vs. number of people who have subscribed to that person's blog (this is just a made-up example). I…
raegtin
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Connection between power law and Zipf's law

I am trying to better understand the connection between the power law distribution and Zipf's distribution (law). There is a neat explanation in [1]. The article suggests that as we can derivate the power law function from Pareto's law, combined…
fsociety
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