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

173 questions
5
votes
1 answer

Intuitive descriptive statistics for power law distributions

For normal distributions we have a set of intuitive descriptive statistics that help us understand how a variable is distributed (mean, mode, median, standard deviation, skewness, & kurtosis). What are similarly intuitive descriptive statistics for…
histelheim
  • 2,993
3
votes
1 answer

How to explain usage pattern that follows heavy-tail distribution to non-experts?

I need to measure and communicate to non-statisticians the usage pattern of a software component. It seems that based on data the usage follows a nice smooth heavy-tail distribution: lots of users don't use the component at all, few users use it a…
iliasfl
  • 2,554
2
votes
1 answer

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, meaning that one family of distributions is a subset of…
RMurphy
  • 866
  • 7
  • 18
2
votes
1 answer

Do histograms need to be sorted to determine if the data follow a power Law distribution?

I am analyzing Twitter response data. I plotted a histogram shown below: As you can see, most tweets get a response fairly quickly. I am confused whether this follows a power law distribution. I notice the J-shape of this distribution. It makes me…
looperr
  • 21
1
vote
0 answers

Is Prices law a consequence of Benford's law?

Background Price's law says this: In an company, half of all value is created by the square root of the people. I'm sure Dr. Price looked at more than the median, but I suspect this was how the technically-illiterate average person could ingest the…
EngrStudent
  • 9,375
0
votes
1 answer

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

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 distribution in a way in which it doesn't matter how…
0
votes
0 answers

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 combine them in this post: How to locate this…
syre
  • 247