A Power Law in statistics is defined as an efficient connection between two measures, where a comparative modification in one measure effects in a proportional comparative modification in the other measure, irrespective of the primary scope of those measures; once measure differs as an influence of another. Copy the link given below and paste it in new browser window to get more information on Power Law:- http://www.transtutors.com/homework-help/statistics/power-law.aspx

1. Power Law

2. Power-Law Distribution
 linear scale  log-log scale
 The above graph represent high skewness , that is
asymmetry
 There are straight line on the other graph where log-
log is plot

3. Examples of Power law
Moby Dick scientific papers 1981-1997 AOL users visiting sites ‘97
bestsellers 1895-1965 AT&T customers on 1 day California 1910-1992

4. Power Law Distribution
 It shows straight line when a log-log plotted, as
 It exponentiate on both sides such that p(x), that is the
probability observed item having size ‘x’, given by
α−
= Cxxp )(
)ln())(ln( xcxp α−=
normalization
constant (probabilities over
all x must sum to 1)
power law exponent α

5. Adjusting the Power-Law Distributions
 Generally used method:
 Different values assigned to x are being binned and
developed into frequency histogram
ln(x)
ln(# of times
x occurred)
Here, x shows different quantities, the indegree of node,
or magnitude of an earthquake
As , we know
ln(x) is the
logarithm of x,
However, any
other base of
logarithm gives
the similar
exponent as
log10(x) =
ln(x)/ln(10)

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7. Hey Friends,
This was just a summary on Power Law. For more
detailed information on this topic, please type the link
given below or copy it from the description of this PPT
and open it in a new browser window.
http://www.transtutors.com/homework-
help/statistics/power-law.aspx