Information AboutPower Law |
| CATEGORIES ABOUT POWER LAW | |
| exponentials | |
| power laws | |
| probability theory | |
| statistics | |
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: where ''a'' (the constant of proportionality) and ''k'' (the Exponent of the power law) are constants. Power laws can be seen as a straight line on a Log -log graph since, taking logs of both sides, the above equation is equal to : which has the same form as the equation for a line : Because both the power law and the Log-normal Distribution are Asymptotic Distribution s, they can be easy to confuse without using robust statistical methods such as Bayesian model selection or Statistical Hypothesis Testing . Indeed, a log-log plot of a log-normal distribution can often look nearly straight for certain ranges of ''x'' and ''y''. One rule of thumb is the distribution conforms to a power law if it is straight on a log-log graph over 3 or more Orders Of Magnitude . Power laws are observed in many fields, including Physics , Biology , Geography , Sociology , Economics , Linguistics , War and Terrorism . Power laws are among the most frequent scaling laws that describe the Scale Invariance found in many natural phenomena. Examples of power law relationships:
Examples of power law Probability Distribution s: These appear to fit such disparate phenomena as the popularity of websites, the wealth of individuals, the popularity of Given Names , and the frequency of words in documents. Benoit Mandelbrot and Nassim Taleb have recently popularised the analysis of financial market volatility in terms of a power law distribution (as opposed to the traditional Gaussian distribution), and Aventis science prize-winning author Philip Ball has argued that the same power law relationships that are evident in phase transitions also apply to various manifestations of collective human behaviour. SEE ALSO EXTERNAL LINKS
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