Statistical Properties Of Continuous Power-law Distributions

Impirical studyings show that most of the real networks possess power-law behavior of the degree distributions. In this paper, we focus on the parameter statistical properties of continuous power-law distributions, consider the parameter estimation, hypothesis test and likelihood ratio test.(1)The parameter estimations of continuous power-law distributions is explored. Maximum likelihood estimation and effective estimation of the parameter are re-searched. A asymptotically effective estimation is given, and it is proved that the effectively unbiased estimation is nonexistent.(2)The parameter hypothesis test of continuous power-law distributions is ex-plored. Uniformly most powerful test and uniformly most powerful unbiased test for the level a are researched in five hypothesis test problems.(3) The parameter likelihood ratio test of continuous power-law distributions is explored. Considering two simple hypothesis and a composite hypothesis test problems for the level a for the likelihood ratio test.