LINEAR FRACTAL INTERPOLATION FUNCTION FOR DATA SET WITH RANDOM NOISE

Mohit Kumar, Neelesh S. Upadhye and A. K. B. Chand
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Mohit Kumar: Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, Tamil Nadu, India
Neelesh S. Upadhye: Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, Tamil Nadu, India
A. K. B. Chand: Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, Tamil Nadu, India

FRACTALS (fractals), 2022, vol. 30, issue 09, 1-17

Abstract: Fractal interpolation is a contemporary technique to approximate numerous scientific experiments and natural phenomena. For data sets in ℠2, the simplest and easy-to-handle fractal interpolation functions (FIFs) are linear. In this study, we estimate probability distributions of linear FIFs for data sets with various types of random noise. In order to evaluate the distribution of any linear FIF associated with a prescribed data set having Student’s t-distributed noise, we develop a technique to approximate the distribution of a linear combination of independent generalized Student’s t-distributed random variables. In addition, we provide some statistical properties and numerical approximations of these linear fractal functions.

Keywords: Fractal Interpolation; Distribution of Fractal Function; Student’s t-Noise; Stable Noise; Random Noise; Heavy-Tailed Distribution (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501869

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