Validating Power Laws
Although power-law relations are attractive for many theoretical reasons, demonstrating that data do indeed follow a power-law relation requires more than simply fitting a particular model to the data. In general, many alternative functional forms can appear to follow a power-law form for some extent (see the Laherrere and Sornette reference below). Also, researchers usually have to face the problem of deciding whether or not a real-world probability distribution follows a power law. As a solution to this problem, Diaz proposed a graphical methodology based on random samples that allow visually discerning between different types of tail behavior. This methodology uses bundles of residual quantile functions, also called percentile residual life functions, which characterize many different types of distribution tails, including both heavy and non-heavy tails.
A method for validation of power-law relations is by testing many orthogonal predictions of a particular generative mechanism against data. Simply fitting a power-law relation to a particular kind of data is not considered a rational approach. As such, the validation of power-law claims remains a very active field of research in many areas of modern science.
Read more about this topic: Power Law
Famous quotes containing the words power and/or laws:
“The dissident does not operate in the realm of genuine power at all. He is not seeking power. He has no desire for office and does not gather votes. He does not attempt to charm the public, he offers nothing and promises nothing. He can offer, if anything, only his own skinand he offers it solely because he has no other way of affirming the truth he stands for. His actions simply articulate his dignity as a citizen, regardless of the cost.”
—Václav Havel (b. 1936)
“The putting into force of laws which shall secure the conservation of our resources, as far as they may be within the jurisdiction of the Federal Government, including the more important work of saving and restoring our forests and the great improvement of waterways, are all proper government functions which must involve large expenditure if properly performed.”
—William Howard Taft (18571930)