On the Statistical Properties of the Deformed Algebras on the Jackson q-Derivative

ÇANKAYA M. N.

3rd International Conference on Mathematics and its Applications in Science and Engineering, ICMASE 2022, Bucharest, Romania, 4 - 07 July 2022, vol.414, pp.249-261 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 414
  • Doi Number: 10.1007/978-3-031-21700-5_23
  • City: Bucharest
  • Country: Romania
  • Page Numbers: pp.249-261
  • Keywords: Algebras, q-calculus, Statistical inference, Tsallis entropy
  • Uşak University Affiliated: Yes

Abstract

The property of Tsallis q-entropy is introduced. The q-deformed logarithm produced by Tsallis q-entropy is examined. In this study, the summation and subtraction based on this entropy and logarithm are extended to the correlation coefficient type. Since a new deformed difference based on the statistical properties such as correlation coefficient and the M-estimation method exists, a new derivative and its corresponding integral can be proposed. The simulation study is performed to observe the results of the proposed algebras which are the summation and the subtraction.