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Linear Fractal Interpolation Function For Data Set With Random Noise

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mohit Kumar & Neelesh S. Upadhye & A. K. B. Chand, 2022. "Linear Fractal Interpolation Function For Data Set With Random Noise," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(09), pages 1-17, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:09:n:s0218348x22501869
    DOI: 10.1142/S0218348X22501869
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