Uniform Minimum Variance Unbiased Estimator of Fractal Dimension

Keywords: fractal dimension, fractal distribution, uniform minimum variance unbiased estimator

Abstract

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.

Author Biography

Elmer C. Castillano, University of Science and Technology in Southern Philippines, Cagayan de Oro City, Philippines

He is the chairperson, USTP  Math Department

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Published
2021-05-29
How to Cite
MaurealZ., CastillanoE., & PaduaR. (2021). Uniform Minimum Variance Unbiased Estimator of Fractal Dimension. Recoletos Multidisciplinary Research Journal, 9(1), 63-68. https://doi.org/10.32871/rmrj2109.01.06
Section
Articles