STATISTICAL ANALYSIS OF FRACTAL OBSERVATIONS: APPLICATIONS IN EDUCATION AND IN POVERTY ESTIMATION

Abstract

We examine the power-law distribution with fractional exponents as a parent distribution of a random sample. The phase plot (xt, xt+1) of the random sample is shown to behave like fractals as defined by Mandelbrot (1967). Two (2) features of fractals are discussed as possible replacement of the mean (μ) and the standard deviation (σ) in describing fractals since the two quantities may not exist for low dimensional fractals 0 < d< 2. The two (2) features are the quantiles and ruggedness measure via fractal derivatives and integrals.