In spite of the purposedly disparate structure of these models, power laws
with exponents close to -3/2 still characterize the dynamics of intermittent rarity [ILLUSTRATION FOR FIGURES 9A, B OMITTED].
The exponents [Beta] and [Gamma] of the power laws
do not depend on the aging time, [Gamma] = 0.
He presents no data showing power laws
apply to business cycle fluctuations, which are the only phenomenon he attempts to model explicitly.
supplement their learning with real-world topics explained through the perspective of probability theory: sports streaks and their correlation to a coin-tossing model; the stock market, with discussion of power laws
and their effects on stock prices; lotteries and the effects of income tax, present value, and sharing on their value; and the use of fingerprints in fighting crime.
Indeed, the absence of a predominant trait is typical of phenomena that obey power laws
, he notes.
Chapters address school vouchers and student achievement, organizations and trade, the importance of history for economic development, the experimental approach to development economics, the economic consequences of the international migration of labor, detecting race bias using statistical evidence, power laws
in economics and finance, housing supply, quantitative macroeconomics with heterogenous households, learning and equilibrium, learning and macroeconomics, sufficient statistics for welfare analysis, networks and economic behavior, subjective probabilities in household surveys, and other topics.
Since the researchers revised it in the June 4 SCIENCE, the theory no longer formally requires a hierarchical branching network--which cells lack--to give rise to power laws
have cropped up across a spectrum that includes patterns of earthquake strengths, heartbeat rhythms, and bird foraging (SN: 8/17/96, p.
Their analysis generates forms consistent with power laws
describing how population in real cities varies with radius and area, and with relations governing their size and spacing," Batty comments in the same issue of Nature.
, Pareto distributions and Zipf's law, Contemporary Physics, 2005, 46, 323-351.
Cont, "Convergent multiplicative processes repelled from zero: power laws
and truncated power laws
," Journal de Physique I, vol.
The power laws
related to the distributions with computational issues and real life examples are presented in a chapter in the first part.