Open AccessUniform Minimum Variance Unbiased Estimator of Fractal Dimension
Author(s) -
Zeny L. Maureal,
Elmer C. Castillano,
R. Padua
Publication year - 2021
Publication title -
recoletos multidisciplinary research journal (online)/recoletos multidisciplinary research journal (usj-r. print).
Language(s) - English
Resource type - Journals
eISSN - 2423-1398
pISSN - 2408-3755
DOI - 10.32871/rmrj2109.01.06
Subject(s) - minimum variance unbiased estimator , mathematics , estimator , bias of an estimator , fractal dimension , efficient estimator , trimmed estimator , statistics , stein's unbiased risk estimate , pareto distribution , fractal , logarithm , dimension (graph theory) , random variable , mathematical analysis , combinatorics
The paper introduced the concept of a fractal distribution using a power-law distribution. It proceeds to determining the relationship between fractal and exponential distribution using a logarithmic transformation of a fractal random variable which turns out to be exponentially distributed. It also considered finding the point estimator of fractional dimension and its statistical characteristics. It was shown that the maximum likelihood estimator of the fractional dimension λ is biased. Another estimator was found and shown to be a uniformly minimum variance unbiased estimator (UMVUE) by Lehmann-Scheffe’s theorem.