Abstract
We examine the power-law distribution with fractional exponents as a parent distribution of a random sample. The power-law distribution is shown to be similar to the Pareto distribution used in statistics for analyzing income distribution. Data roughness is described in terms of a fractal dimension (λ) which always exists even in cases where the variance (the usual measure of variability) may not exist. Estimate of data roughness for each observation xi is provided. The statistical properties of the fractal dimension of a random variable X are explored. Visual representation of data roughness are likewise provided.
Recommended Citation
Padua, Roberto N.; Palompon, Daisy R.; Ontoy, Dexter S.; and Barabat, Enfren O.
(2012)
"Fractal Statistics and Data Roughness,"
CNU Journal of Higher Education: Vol. 6:
Iss.
1, Article 7.
DOI: https://doi.org/10.70997/2546-1796.1138
Available at:
https://jhe.researchcommons.org/journal/vol6/iss1/7